Air movement is a tricky subject. I got asked about this subject by our good friend like over a week ago, but I've not tried posting about it. I'm certain this will be a two or three post subject, surely.
The thing about airmovement is that it can really make or break things, depending on how things are implemented. A perfect example of both types of airmovement miserably failing would be Big Bang Beat. But possibly (depending who you ask) the greatest example would be Scarlet Weather Rhapsody, since it implemented almost-free 8-way movement in the air.
A good example of it actually working is probably Marvel vs Capcom 2 and Monster.
I believe the biggest issue with implementing either feature is how you implement various types of attacks and also guarding or airthrows in the air. If these are done poorly then it won't matter how you do air movement, the game will not be fun at all due to how linear and predictable things become.
The first thing that comes to mind is that SWR and BBB do not have airthrows, while standard and popular games do. Everything from Street Fighter to Melty Blood and Guilty Gear.
Now, SWR's predecessor game, Immaterial and Missing Power, also does not have air throws. But it also doesn't have 8-way air movement, only horizontal airmovement and no double jumps. I think that's a very important distinction.
Therefor, I'd like to first address doublejumps, and save airdashing for a later time.
The thing about doublejumps is they take the "rules" and a lot of the footsies mechanics that beat/break the "rules" that I was talking about in my previous post.. they take them and they throw them out the window. But only if the game doesn't support everything it needs to counter-balance doublejumps.
One golden-rule example is the jump-in. A player shouldn't just be allowed to jump at an opponent when both players are simply standing there doing nothing at around jump-distance. They should have to put the opponent in a situation where they are unable to anti-air by taking some measurement of risk. The other player should be able to anti-air them consistently and easily if they do not do anything strategical to achieve it. With double jumps this becomes a lot more complicated, you can jump again in the air right before getting anti-aired to avoid getting hit, and fish for anti-airs.
Another golden rule is risking a knockdown while moving forward. Dashing is obviously more risky than walking. But with doublejumps why bother with either when you can first move forward but jumping, then doublejump vertically and stay your ground, inching forward very safely.
These are major problems that designers have to deal with, balancing out things for both characters and game mechanics.
Fact is, if your character has a crouching light attack that can be rapidly spammed and works as an anti-air, while another character has only one valid anti-air that is a special move that takes them off the ground, things are unbalanced in this situation. Without doublejumps it probably isn't so extreme, but with them implemented then it definitely is polarized.
But, you can't just give the entire roster easy-mode light attacks that are anti-airs or that would defeat the purpose of doublejumps in the first place by destroying the point of being in the air at all. And if you're playing with balance by giving it to some but not others then you're inevitably fucking over the tournament scene unless you're a super genius (in which case you wouldn't be reading this) and can balance out every little thing.
However, it's not impossible to counter-balance doublejumps. As mentioned earlier, airthrows play a pretty big role. Another thing that really makes a difference is airblocking, and more specifically the lack thereof. But probably the biggest difference is the height of the doublejump itself and the overall priority/control air attacks have.
You could assume that 8-way movement is a sure fire way to fuck a game up, but it's actually hard to say. Jojo's Bizarre Adventure and MvC2 gave it to some characters, and SWR gave it to the whole roster. I'm of the finalized opinion that 8-way fucked SWR for good due to the terrible options for dealing with it. But it didn't exactly screw Jojo's and MvC2 entirely, and both games implement both pushblocking and guard canceling. It did, however, bring the characters that had this ability to the top of the tiers. Magneto and Kakyoin being the most celebrated in this regard. You could talk all day about how both characters have everything plus a bag of chips (Kakyoin, anyway), but I can guarantee you that Kakyoin isn't dominating just with his range alone.
Though, if you know anything about these games then you'd probably know that there's almost never any wiggling or ground-based footsies going on in them. Players will either rush in or fish aimlessly/wildly until they can begin the rushdown process, thus turning the game into a widely momentum based game.
I don't want to just go and say that it's an on/off switch though. As in, with doublejumps-footsies die. And the reason I don't want to say it is because Monster showed me that this is not the case.
The thing about Monster in particular was that doublejumps were very very short and low, they weren't actually a second jump at all but more of a little hop that changed your air trajectory. Additionally, even though Monster didn't have airthrows (cept for air cmd throws), it also did not have airblocking which alleviated most of the need for air throws (not entirely though, IMO).
You'd think that low doublejumps would be counterproductive, as in, I use to think that the extremely high doublejumps found in MB weren't problematic because anti-airs ended before the airborne character regained their position, but I was dead wrong and they sure as hell are problematic.
On the flipside, Monster's doublejumps weren't problematic at all except for how they affected combos. But for the most part, it didn't degrade or dilute footsies or how anti-airs worked. There was really only a few characters that had really poor anti-air options, the rest of the cast could deal with it just like any other game.
But this is where the on/off switch actually does occur, as far as I know. If a game is given 8-way air movement then it needs some ridiculously extreme defensive options to deal with it like pushblocking, guard reversals, instant blocking, assists, etc. If a game is given high double jumps then it turns into something like MB where players tend to hop around totally aimlessly, simply trying to stay above their opponent at the right time and fish for random hits.
In the end, the goal should be to preserve footsies while maintaining doublejump functionality. And frankly, most games do not, Monster being the only one that I can really think of that has both a strong footsie game and doublejumps implemented.
But even in games like GG you get matches where both players are hopping around in the air for almost no rhyme or reason other than to fish for random hits.
And that brings us back to the subject of airdashing, which I'll have to address later. Sorry for the currently scattered post, I'll have to revise it later as well.