Dvorak and Colemak are made to do the same thing, move commonly used keys on the home row. And they both did that as about as good as the other. Between those two I would say Colemak is better for most because It is made to have similarities with Qwerty while still being as good as Dvorak. I personally use Dvorak though.

Another relatively known layout is the Workman layout. This layout makes it so the most commonly used keys are placed in a hand shape possibly making it even more ergonomic than Dvorak and Colemak. Norman is also similar to Workman except for Norman is made so right hand is used more frequently assuming right hand is more capable due to being dominant for most.

In terms of speed, It is hard to say how much it exactly increases due to the lack of data, but I've experienced huge speed increases since I switched to Dvorak. And in theory, it makes sense these layouts will give speed benefits compared to Qwerty because there is less hand movement. But I've heard many people where they couldn't commit to it enough to get faster than Qwerty. Either way, in my opinion, I will take Dvorak over Qwerty even if I am slower on Dvorak because of the huge benefit it gives to comfort.

edit: I forgot to mention that there is such thing as a chorded keyboard, most commonly stenotype. These have a huge disadvantage of a learning curve, but some people are able to input 300+wpm consistently. I've been taking attempts of learning stenotype using an open source software called plover, but I can't even type a full sentence yet.