Logically, Xigbar would win. He has guns that shot several dozen bullets in quick succession, whilst Axel has two wheels that shoot fire. Xigbar controls Space and as such, can easily teleport away from Axel and snipe the flaming Nobody right between the eyes.
Axel's fire teleport move would have little effect when his movement is constricted by Xigbar's space element. His thrown chakram would be easily dodged and he would quickly be punished for it with a hail of laser bullets.
In short: Xigbar wins.
P.S: You people know that this is not a popularity contest right? It's a question over who would win logically, not just because you like them more.