Good zombie apocalypse rule set?

I've been GMing in a few different systems off and on for a while now. All of the stuff I've done recently is more fantasy-based (lots of D&D, some Upheaval, a little Pathfinder). The only modern setting stuff I've ever done was Top Secret, but that was a long time ago.

I've had a desire recently to do a modern setting zombie game. I've seen a lot of sets (All Flesh Must be Eaten, the Walking Dead, GURPS and Savage Worlds). I've never played any of those, though, and I'm not sure which one to go with. I did look at the game recs list, and that just gave me more analysis paralysis. The End of the World looks intriguing.

I want to run a game that starts with the outbreak, and has a good balance of fighting zombies & survivors, gathering resources, and trying to survive. I want a system where we roll dice; I like the random element that provides. I am looking for the ability to make the game pretty long term. Most of my campaigns last upwards of 70 sessions. I've had a few that went almost to 200.

So, for those of you who have run a zombie apocalypse game, what systems have you used? What did you like about them? What did you dislike? What would recommend I try out?