Why does the Torah write that "Aharon's staff swallowed the staves of the magicians," and not that 'the snake swallowed their snakes'?
Rashi: Because it was only after all the snakes turned back into staffs, that Aharon's staff swallowed theirs. 1
Seforno: In fact, it was Aharon's snake 2 (which was alive) that swallowed those of the magicians (which were lifeless) - to demonstrate that it is only Hashem who is capable of providing life. 3
Rashi (to Shabbos 97a), cited by Gur Aryeh: This is 'a miracle within a miracle.' Hadar Zekenim - Also, it did not become thicker after swallowing them (It is not clear how the Hadar Zekenim knows that!). Pharaoh was afraid that it would also swallow him and his throne!
Presumably, the Pasuk refers to the staff of Aharon, because strictly speaking, it was not the snake that belonged to Aharon but the staff - turned snake.
Why did the fact that Aharon's staff swallowed their staffs not convince the astrologers of Hashem's superiority?
Oznayim la'Torah: Because they could argue that, had they known that Aharon would command his staff to swallow their staffs, they would have commanded their staffs to swallow his - and that they would have succeeded. 1
Gur Aryeh: Pharaoh knew full-well that sorcery could not accomplish this! Refer to 7:13:1.1:1.