Gemara

(Mishnah): If one said "Alai (it is encumbent on me to bring an) Olah," he must bring a lamb (or a bigger animal);

R. Elazar ben Azaryah says, he may bring a Tor or Ben Yonah (a bird).

Bava Kama 78a - Question (Rava): If Reuven said 'Alai Olah', and he separated an ox for this, and it was stolen, can the thief exempt himself by returning a lamb (according to Chachamim) or a bird (according to R. Eliezer ben Azaryah)?

Since Reuven never specified what type of Olah he will bring, the thief may return any valid species;

Or, perhaps Reuven can say 'I intended to do an ideal Mitzvah (a big Korban. Therefore, you must return a big animal.)'

Answers (Rava): The thief can exempt himself by returning a lamb or bird, according to Chachamim and R. Eliezer ben Azaryah, respectively.

Rishonim

Rambam (Hilchos Ma'aseh ha'Korbanos 16:7): If one said "Alai Olah," and he separated an ox, and it was stolen, he can exempt himself with a lamb.

Shiltei ha'Giborim (Bava Basra 6a:2 DH umeha'Hi): Bava Kama 78b teaches that if one was Noder (vowed) and separated a large (animal or gift to Hekdesh or a Beis ha'Keneses or Tzedakah) and it was stolen, he is Yotzei with a small gift. The Rambam rules like this. Similarly, the thief can exempt himself with a small one, since the Noder is Yotzei with it. We learn from here that if Shimon borrowed something from David, and Levi stole it, and David pardoned Shimon for less than its value, Levi pays Shimon only what Shimon paid to David. If David was a Nochri and he pardoned Shimon, Levi is exempt, for Shimon did not lose. It is not clear whether one may rely on this in practice. We say oppositely that if David demanded more than its true value, if the item is not intact Levi pays only its value. Rashi explains that the question was according to R. Shimon, who says that it is as if he stole from the Noder. If he stole from Hekdesh, Hekdesh did not lose anything, since the Noder is still obligated. However, perhaps Hekdesh can say that he caused a loss to Hekdesh, for now perhaps the Noder will bring only a lamb. Since the Halachah does not follow R. Shimon, according to this the thief must pay an ox. The Rambam rules that the Noder is exempt with a lamb. The Gemara connotes that Rava answered his question, which was about the thief! Perhaps the Rambam had a different text.

Maharam Mintz (113): If Reuven bought a big Esrog for Hidur Mitzvah for a high price, and Shimon destroyed, disqualified or took it, he must buy another Esrog for him. It suffices for Shimon to give to him a Kosher Esrog; it need not be Mehudar. We learn from Bava Kama. Even though the Noder wanted to bring a choice Korban, the thief exempts himself with a lamb. The same applies here. However, Shimon must pay the increased value of a large Esrog after Sukos (for eating). Why can the thief exempt himself with a lamb? The skin of an ox is worth more! Do not say that the skin goes to the Kohen, and not to the Noder. The question was Stam, i.e. even if the Noder is a Kohen, who can keep the skin! Rather, also there we do not discuss monetary damage. Obviously he must pay any monetary damage (e.g. if the Noder was a Kohen). The question was regarding Hidur Mitzvah, whether he must give to him an ox (to offer). If the Noder was a Yisrael, there is no monetary damage. Do not say that the Yisrael can say 'I wanted to wait for the Mishmar of my relatives.' We hold that Tovas Hana'ah (the right to choose to whom to give Matanos Kehunah) is not considered Mamon (one does not own it). Regarding an Esrog, there is a real monetary loss

Mishneh l'Melech: If Reuven bought an Esrog for a high price, and Shimon stole it and disqualified it, can he exempt himself with a Kosher Esrog less nice than the first one? Can he say 'if not, not for the Mitzvah, the Esrog is worth only one Zuz. Your only obligation is to fulfill the Mitzvah. You can fulfill it also with this Esrog! Or, perhaps Reuven can say 'I want to do an ideal Mitzvah.' It seems that we learn from Bava Kama. The thief exempts himself with a lamb. Reuven cannot say 'I want to do an ideal Mitzvah.' However, it seems that these are different. The ox had no Damim (price), because one cannot sell his Olah or Shelamim. The thief's Chiyuv is only so that the Noder can fulfill his vow. Therefore, a lamb suffices. Here, Reuven could have sold his Esrog for the same price he bought it for. Shimon must pay the money that he made him lose. I saw that Maharam Mintz learned from Bava Kama. Shiltei ha'Giborim is astounding.

Admas Kodesh (1 CM 64): Reuven borrowed Shimon's Tefilin in order to pray Shacharis. Rav Uchna wrote them, and they were very valuable. He told this to Reuven. They were lost. Shimon demands that Reuven buy another pair from Rav Uchna, and if he cannot, to pay their value. Reuven says that it suffices to return Tefilin that are Kosher without any Safek. Bava Kama 78b supports Reuven. The Rambam teaches only that the Noder can exempt himself with a lamb. He omits the Gemara's primary teaching, that the thief exempts himself with a lamb. It seems that he holds like Rashi, that the question was according to R. Shimon, who distinguishes between Kodshim with and without Acharayus. According to Chachamim, surely he exempts himself with a lamb. Chachamim exempt from paying Kefel (double), four or five; the difference between an ox and lamb is like this. The thief can say 'I did not steal from you, rather, from Hekdesh.' According to R. Shimon, if the Noder has Acharayus, it is like his property. The Rambam rules like Chachamim. We learn from Maharam Mintz that it suffices to return Kosher Tefilin. The beauty of the boxes, writing and straps must be the same, just they need not have the Hidur Mitzvah (of the intents of the Rav who wrote the first Tefilin).

Admas Kodesh: R. Shangi asked that the question is even according to Chachamim. R. Shimon and Chachamim argue only about Kefel, four and five. All obligate principal (Rambam Hilchos Geneivah 2:1). The Magid Mishneh says that Rashi agrees that the thief is liable, like anyone who was Mo'el. The Gemara discusses his Chiyuv to the original owner. Chachamim exempt, for it was not his. R. Shimon obligates, and we asked whether the payment of Kefel is an ox, or a lamb or bird. I disagree. If so, what is the Noder's claim 'I wanted to do an ideal Mitzvah'? Even if the thief pays Kefel, four or five, he pays them to Hekdesh! The Noder gets only principal. The Poskim did not discuss this, but there is no source to say that the Noder offers Kefel, four and five. He already received atonement! He wants to do the ideal Mitzvah. I.e. in a place where Stam 'Olah' refers to an ox, he must bring an ox. Perhaps the Noder was unsure about whether in his area, Stam Olah is an ox.

Poskim

Shulchan Aruch (OC 656:1): If one bought a Esrog that is minimally Kosher for the Mitzvah, e.g. it is just a Beitzah, and afterwards he found a bigger one, it is a Mitzvah to add up to an outer third (half the principal) of the price of the first one.

Eliyahu Rabah (1): If Shimon disqualified Reuven's Esrog, he must pay only a small Esrog Kosher for the Mitzvah. However, he must pay the increased value of a big Esrog over a small one after Sukos.

Birkei Yosef (2): Maharatz (120) obligates paying the full value of what he disqualified.

Rebuttal (Chacham Tzvi 120): The ox had no Damim, because one cannot sell his Olah or Shelamim. Here, Reuven could have sold his Esrog for its value, even though this is due to Hidur Mitzvah. If one stole a Sefer Torah worth 1000 Zuz due to its Hidur, i.e. beautiful parchments, ink and an expert scribe, he cannot exempt himself with a Sefer Torah worth 50 Zuz, just because one is Yotzei with it the Mitzvah "Kisvu Lachem Es ha'Shirah ha'Zos." This is logical, and there is also a proof from the Gemara. If he could exempt himself with a minimally Kosher Sefer Torah, Rava should have taught this Chidush, for a Sefer Torah has Damim. If one sold it, it is sold, and one may sell it even l'Chatchilah in order to learn Torah or marry. (Rather, it is not true, therefore he taught about an Olah.) However, do not reject Maharam MIntz because we hold that Rabanan of R. Yehudah, who say that Ona'ah applies to a Sefer Torah. It seems that this is even if the seller was underpaid. I.e. it is like other Metaltelim, and we estimate its market value. The buyer cannot say 'I will return to you another Sefer Torah worth half the amount.' Therefore, Ona'ah applies to it, like to other Metaltelim. Maharam Mintz could say that this is unlike something that one wants to use for a Mitzvah. However, I refuted him above. Also, if we would make such a distinction, one who stole an Esrog from a vendor must pay its full value, but one who stole from one who bought from the vendor, for the sake of the Mitzvah, would pay only one Zuz, i.e. the value of a small inferior Esrog. Such matters should not be heard. Rather, one who steals an Esrog before or during Sukos pays its value.

Mishbetzos Zahav (1): If Shimon stole Reuven's Esrog, if Reuven seized from him its full value, he can keep it and say 'I am sure that the Halachah follows those who say that he must pay the entire value.' However, if Shimon unintentionally disqualified it, even the Chacham Tzvi would agree that he exempts himself with a small Esrog.

Bikurei Yakov (3): The Shitah Mekubetzes (Bava Kama 78b) says in the name of the Ra'avad that if the ox is still intact, the thief must return it. Similarly, if the thief has the stolen Esrog, he must return it. He cannot return a small one. I defend Maharam Mintz. Even though one cannot sell his Olah, it is worth money to him. We say that one can make his Kodshim Cherem. He pays its Tovas Hana'ah to him, i.e. what it was worth to him to offer it (Erchin 28b). Since he could have been Makdish a lamb, but he was Makdish an ox, this shows that he wanted a big Korban. Also to others an ox is worth more than a lamb. This is even according to the opinion that Tovas Hana'ah is not Mamon. Even so, the thief pays only for a lamb. The same applies to Esrog. This law requires investigation.

Tzitz Eliezer (11:82): Shevus Yakov (2:29) agrees with the Chacham Tzvi, but adds that if there is no one around who would buy it for the its value, even if it is exceedingly Mehudar, and the buyer added an extra third for Hidur Mitzvah, the thief does not pay for this (only for what the owner could have sold it for).