Argosax was the previous ruler of the demon world prior to Mundus' usurp to power and Argo's banishment to the outlands of the demon world.
Now obviously we could argue that Mundus is stronger because he defeated Argosax, but since he didn't actually kill him, it's most likely that he wasn't able to for whatever reason.
(If he destroyed his physical form, it's possible that Mundus didn't have enough power to completely and utterly destroy him)
At the same time, as others have said before I, though Dante was easily able to defeat and/or "kill" Argosax in DMC2, that's mostly not only because of the difference in difficulty level between the first and second games, but also the fact that Dante was much, much stronger in DMC2, possibly even more powerful than Mundus and even Sparda and therefore able to defeat Argosax easily.
So, to me, it could go either way honestly.