Shouldn't be unfair if the poll is simply about how you feel subjectively about each game. I'm simply asking what everybody thinks is a better overall game. i.e., what you personally have more fun playing. For that matter, I could ask the same thing about two games that are WILDLY different, like Street Fighter II and Son Son II. Both are great games, but I personally find SF2 more fun to play. That being said, LA and LA2 are clearly in the same genre of side-scrolling hack-n-slash platformers, so comparing the two should be slightly easier.
I went with Legendary Axe 1. LA2 has better sound, but I was never a big fan of the graphical style in LA2... too much "pillow shading" and weird color choices. I'm not saying LA1 has killer graphics. In fact, when I first played LA1 20 years ago, I was pretty underwhelmed with the graphics. The main factor, however, was the fact that LA1 seemingly has more responsive controls. In LA1, if you press the jump button you jump almost immediately (2 game ticks). In contrast, in LA2 if you press jump, it pauses a split second before you jump (a full 6 game ticks before you get airborne). That gets annoying in certain parts of the game, especially near the end.