First of all: Great work to the both of you.
Flinch: Great animation and awesome angles, the fight was entertaining but the ending left me a tad puzzled. If both chars could fall down a tall building, bash into the window and still be pretty okay, why did pushing Hex out the window make it a victory? In short, I think you should have emphasized that "Now, hex has been defeated." Like the beam perhaps piercing through his stomach and out his back perhaps? The background was pretty basic but it certainly set the mood alright. The grey background made the skyscraper blend in and it looked pretty depressive. Thats not a bad thing, it made the battle seem pretty desolate, despite being good, try to take that concept to new heights!
Hex: Your style is quite clean and tidy, not that gritty. That has its ups and downs. I think the battle was depicted a bit too "anime-ish" the battle consisted of power-attacks all the time. I think you need to take power-attacks down several notches, sure they're awesome; but if you sell them like butter, it won't feel any special when they're preformed in your animations. The art style and cinematic angles were really good but somehow I felt the story was hard to follow. Why did the battle go a few weeks forward? Was it the same place? I think you need to give your viewers more information! ^^
With all that said: I vote Flinch's anim! It entertained me more but I wish you both best of luck. :)