An AR10 seems awfully heavy. Almost 8lbs not counting optics, ammo, accessories, etc which I guess would add around another lb or two. On the other hand, for most situations I doubt that many people would accuse you of not bringing enough gun.
Of course if you knew what the situation was going to be you could cater your tools (including guns) to that situation. For a general purpose survival gun, a 12 or 20 gauge shotgun with something like a PolyChoke on it would make a great gun. You would be able to fire a variety of projectiles like different sizes of birdshot for small game hunting, buckshot and slugs for bigger game or defense and the polychoke would let you vary your pattern to suit the situation. Another plus is that decent tough shotguns are relatively cheap to buy and there are all sorts of accessories like saddles to hold more shells, folding and collapsing stocks, lights, forward grips, aiming devices, etc. Plus, if you've got time to set up a bug out bag that you're grabbing too, there are special loads like signal flares, "bird bombs," etc. that you can shoot out of shotguns. There are even chamber adapters to shoot other gauges/calibers out of shotguns, although I've never used one and they seem like they might be more of a novelty than something that's really useful.