That's a tough call. The Walking Dead: All Out War is kind of like 70 percent board game/30 percent miniatures game. While Fallout is 30 percent board game/70 percent miniatures game. WD is quicker to get into (the manual is only about 12 pages of actual rules), while FWW is closer to 50 pages of rules...and then an additional 30 pages for solo and campaign rules (how to handle the sol AI, how to build a force, etc).
Here's a short description of both:
WD:AoW - You assemble your survivors using the cost listed on each card. Every group has to have a leader, and they all have to have the same faction keyword (also easily found on each survivor card). Then you put down the paper mat (or whatever you're using...you can go hog wild with accessories with either game) and some terrain (they include some flat cardboard terrain that's perfectly functional). Finally, you assemble an event deck that you draw from that serves to move around the walkers and spring surprises on you. This deck isn't terribly big, so you're not going to get an adventure game level of randomness out of it, but it is sufficient to create tension and some ill timed catastrophes that force you to make some hard decisions. You also put down a threat tracker that starts off on "All Quiet". That goes up every time there's noise, and event cards often have multiple options that trigger depending on the tracker's level.
On your turn, you move either 4" (sneak mode) or 8" (your "HEY, I"M OVER HERE, COME EAT ME!" mode). If you move the former, you don't generate noise, thus you don't raise the threat. The latter (along with melee, gunshots, etc.) raise the tracker though. After that, you put a round template with a hole in the middle called the "kill zone" over the heads of all the walkers. If you're within that circle, they lunge at you. If not, they don't do anything (but event cards will often move some or all of them).
Then you melee, draw an event card and stand up any walkers that didn't die from head shots/head blows. Combat is simple. You roll a number of dice according to equipment or number of walkers, figure out the difference, then lose hit points or kill walkers depending on the winner.
The best review I've read for WD: AoW is one in which they pointed out that the walkers in this game are NOT your primary enemy. He dubbed them "mobile terrain", which makes perfect sense after one game. They're not particularly dangerous on their own, but you may have to brave a horde of them to get where you want to be...and that's when it gets dangerous.
There are scenarios that make it much more interesting that what I describe, but as you can tell, it's not a terribly complex game. You'll know all there is to it after 15 minutes, most likely. But it's very thematic. There's a solo centric set called Welcome to Woodbury that adds the Governor and some solo specific material (including an event deck designed for solo) but it's not necessary.
They released a collector's edition a little while back that appears to have all but disappeared, but you can still get the base 2 player starter for less than 40 bucks from more than a few places. I've even seen it for less than 30. The minis do NOT require assembly.
Fallout WW - You assemble your group just like any other minis game, but you have to refer to an online resource that's updated somewhat regularly with new unit/equipment costs meant to reflect balancing that arises as more and more folks play.
This game has a LOT of tiny tokens. There's tokens to show activation, damage, radiation, reactions, charge bonuses, etc. etc. etc.. Fortunately, functionality is pretty easy to spot at a glance.
On your turn, you get two main actions. Move, shoot, melee, special action (hack a computer terminal, crack a safe, etc.) or just prepare (set down a reaction token showing that if someone does something within your sight range, you get a quick action after they do so).
What's really great about this is the way they handle range and success chances. For the former, you have a series of different colored sticks that vary in length. On your character cards/weapon cards, you look for a little bar of one of those colors that shows you the range for whatever you're doing. So for example, your movement is denoted by a small green box. That means you take the green stick and place it in front of your model, and then move the model so that its base is at the head of that stick. For shooting ranges, you usually have two colors side by side. The first is close range, the second is long. Underneath each colored box are bonuses or penalties that use when rolling for success.
Rolls are done with a 20 sided die called a "skill die". Then you add any number of multiple dice with different colors that can add or subtract from your base skill rating, give you extra quick actions, or even trigger special effects (setting your target on fire if using an energy weapon).
That's a VERY low level look at Fallout WW. It's a very deep game. Maybe not as deep as a Warhammer 40K, but definitely much deeper than Walking Dead. It has a very detailed solo AI that uses a grid system on AI cards for each unit that you roll against to determine actions. In my 3 or 4 solo games, I've been very impressed by the "intelligence" of NPC units...even when it comes to situational actions.
It's also about twice the cost of WD: AoW. As I mentioned earlier, I managed to get mine at half price during a holiday sale though. I also see miniaturemarket putting Fallout WW stuff on their "drop" list (items that drop a certain percentage each day until they sell out).
For me, both games scratch an itch. WD: AoW is for those quick to play, short games that give you a real sense of fighting zombies; while Fallout WW is a longer, much more intricate game with a full campaign mode (you can build a settlement over time using the bottle caps you get from winning matches. The buildings in your settlement then determine what kind of equipment, bonuses, etc. you can take with you. It even gives you the chance to draw a little mini adventure card that can give you a reward along with a lot of game flavor.).
So, in summary: WD: AoW if you want a simpler tabletop game that's less work but doesn't really lend itself to more than one off sessions...albeit very fun ones; or Fallout WW if you want a game that can be as deep as you want it to be...at the cost of a lot of rules referencing until you get it down (although to be fair, a lot of it does become intuitive after a game or two).
p.s.
quick start rules for WD: AoW
quick start rules for Fallout WW (you'll have to register to download, I believe)