Typically I talk about AWDS in terms of the default game mode; that is, two or more COs/Tags duking it out on the default victory conditions and game settings, and generally assuming that Force Ranks are not involved. All of these dramatically change to focus of gameplay and heightens the importance of skill, but what difference does it make to the game's balance? Surprisingly little, actually.
As far as Force Ranks go, you will quickly find yourself gravitating to the money skills. In fact, the money and hard-mode skills so eclipse the others in power most of the time that you'll hardly find a use for any of the others. If everyone has the money skills and Soul of Hachi, then the differences come back down to their respective CO abilities. (There are exceptions; they will get their own post.)
Fog does nothing, not even for Sonja. The ability to see further can't save you from mass damage, nor from two moves, nor from insta-capture, mega defense, etc.
Weather can give some weight to Drake and Olaf. Slightly. Olaf can occasionally get more firepower out of the deal, and both can change the weather to suit them. Constant snow can even bump Olaf up within the mass damage circle. But that's really it. Rain is basically Fog especially if it's constant, and Sandstorms don't really do anything except nerf Grit... not that he needs nerfing.
Turn and capture limits just mean that the game ends in the middle of the battlefield rather than at one player's HQ. Alternatively, it can be like Capitol Risk in which the elimination of all players is unnecessary. (Although it one person was getting double-teamed this may not be quite enough.) It can give some weight to Sami, but that's about it.
And lastly, funds. Minor changes to funds can significantly impact the flow of the game. A small bump to 2k funds makes Black Bomb warfare an option. From there it only gets crazier until Tanks and B-Copters finally become endangered species. In spite of the changes to whatever units are on the field, the tactics will be more or less the same. Much of what goes on with funds deserves its own post, but suffice it to say that while it makes the game much more interesting, it doesn't really alter the effectiveness of the COs by all that much.
Lest I forget, I guess there's also the never-talked-about Dual Screen mode. You know, the option in the versus menu to go with either one or two maps? Yeah, I nearly forgot about it myself. It also shares a trait with the other game modes: It doth not affect the gameplay much. A sufficiently powerful CO can lose his partner on the top front and still win down below. They could also send a large amount of reinforcements to the top to keep that from happening... but why bother? You may as well play a single map for all the difference this mode makes.
So basically, while the different game modes can make the game more interesting and change the tactics and focus, the overall game balance remains mostly the same regardless.