The towers and what's special about them:
Civilian: Has a lot of sidearm ammunition (.44, M4A3, and sawed-off/12-gauge shotgun ammo). Doesn't have as many actual *weapons*, however, so if you're looking for a .44 to replace that pansy M4A3 you should probably look elsewhere.
Storage: Has a lot of ammo, medkits, and grenades, as well as a fair amount of weapons and armor. You'll probably find your first .44/nice armor/nice primary here, but beware: you can only see about 5 spaces around you, meaning that if you don't take down the aliens you see fast they will tear you apart. Personally, though, I think this disadvantage is far outweighed by the copious amounts of ammo and medkits, and for that reason (if possible) I make it a habit to stay in this tower as long as possible.
Military: Has advanced armors, some of the nicer primary weapons, and all the heavy weapons. Visibility is reduced, but not as much as in the Storage tower. It's a nice place for what you get, I suppose, but it doesn't seem to have enough ammo to really support me when I look for better weapons.
Medical: Has many medkits, and according to some people has less aliens than the other towers. Probably not the best place to replenish ammo if you're not finding enough to break even, though. (I don't spend much time in this or the next tower.)
Engineering: Currently not all that useful, but in the future will have workshops where you can modify your weapons/buy extra medkits/etc. AFAIK, however, right now all it has going for it is a slightly reduced alien count, as well as a fair amount of common ammo types.
Main: The biggest distinguishing feature of this tower is that the Queen is on level 8 of this tower. Other than that, not a whole lot different than the other towers AFAIK.
One last thing: If you enter a tower and the computer warns you of radiation, that means that your health will gradually decrease every few turns or so that you remain in that tower. To stop losing health, you have to either use an elevator or head off to a different tower. Anyone with a more complete listing of differences may feel free to correct this. I generally don't visit Main, Medical, or Engineering at all unless I have to..