So now that I've played a bit, I think I'm ready to put together my impressions for people.
I don't really get a Super Smash Brothers feel from it. Like cript suggested, it's a lot more like those sidescrolling flash games. You get points for playing which you can use to unlock new weapons, skins for said weapons, costume pieces, and characters. So far there's only four characters and a small selection of costume items. All items are currently shared between characters, so you only have to buy something once.
The only difference between the characters is their basic appearance, lines of dialog, and special ability. Currently there's only one ability for each guy and you can't change it, but I'm guessing that'll change before long. Dutch McClone is a time-travelling Austrian Kindergarten Teacher, and his ability is temporary shield. Hailey Skye is a hacker/explorer chasing her father's secret experiments, and her ability is a rocket jump which is rad and probably the best ability in the game. Mr. Shur Foo is Pai Mei and also Mr. Miyagi, his ability is a kick that does a shitload of damage. Sergeant Lance Koboldski is a cop who's too old for this shit, and he can heal by eating a donut.
Melee is pretty simple, you swing and you block, and you can also throw but people rarely throw. The guns are a little more varied. Pistols are the "balanced" weapon, which is a video game term meaning they suck. Machineguns don't do a lot of damage but they have all but unlimited ammo. SMGs are the fastest gun, but only have enough ammo to kill one guy, in 2.5 seconds. Shotguns are slower than pistols but do more damage, and seem to interrupt you a bit. I've seen a few people do well with them but they don't seem all that great. Rocket Launchers take a long time to aim and fire and are easy to dodge, but will kill you in one hit.
I like SMGs the most. There's a couple other important mechanics, you can heal yourself over time which can make the late game last-man-standing showdowns very passive. So far it seems like the lag isn't too bad, although game hosts almost always win, which is a little suspicious. The combat's simple enough to pick up in a few minutes, but it's that kind of fun that keeps you playing despite the relative lack of depth.
One thing I really like is that all ambient music in the game (elevator music, for example) is remixes of the main theme. Even in the chapel you can hear the monks chanting the theme.