To be honest the combat in Battletoads seems more complex than SOR4's. Looks like you have even further juggle opportunities, you can dash, you can evade, you have a secondary attack, you have charged attacks, you have a launcher and even got a DMC4-inspired move where you can pull enemies towards you with your tongue (or push yourself towards them). SOR4 is more like a classic beat 'em up, and BT seems more modeled after all the Devil May Cry-ish 2D games that have been released in the last 10~ years.
The thing is with three players on screen the action is totally chaotic, especially with the art style they've gone with. I would stop showcasing the three player action, or even better just make it 2P. It doesn't help that in this video the players are literally mashing buttons the entire time even when they don't have enemies in front of them, which probably makes the game look like even more of a mess. The video in the OP is genuinely bad, but it's not because of the game itself, at least not entirely. The players are being almost totally mindless.
I'm not convinced BT is actually awful, the combat system seems to have some thought behind it. The one thing that is definitely a terrible choice is that you can't attack enemies when they're down, which was CLASSIC Battletoads. Who doesn't remember running and punting enemies off-screen, or hammering them down in the ground in the old games? Even worse, in the new BT they spend a heck of a lot of time laying on the ground, being invincible, while you stand around basically not being able to do a damn thing, waiting for them to stand up. This shit's just poor. If you don't want to implement down attacks in the game that's fine, but make them stand up immediately then. This is one of the bigger problems with the game, that it doesn't resemble Battletoads mechanically or visually.
Unlike most, I don't have a single problem with the art style, but they really need to be more judicious in how they show the game next. If they actually have some platforming in the game, they should definitely show that, and they should try to make the combat a little more Battletoads-like by putting down attacks in the game, at least.
Double Dragon 4 is terrible (if that's that's game you were referring to), but Double Dragon Neon is great.