I haven't played All Flesh, but I've run it. I'm a big fan of unisystem and this is no exception. I'm not sure how well All Flesh would do as a campaign, but that is just personal preference with setting longevity. Basically, i have a hard time seeing a world run over by zombies game not becoming repetitive, but for your idea. But, that is just my cup of tea. For your idea, the system will work great. It certainly allows for diversified characters and has been a blast each time I've run it. I tend to look at the combat as incorporating some of Feng Shui's flexibility. If you can describe your action, you have a chance of doing it (not saying it is a very big chance, but it is a chance none the less).
Plus, simple system to learn. They go a little further with all of the different options for dice. I tend to just stick to the dice rules they use in the Buffy & Angel RPGs (just a d10). Makes things simpler.