ID:1996170
 
Which one is the most efficient?
None of them, really. They all just add a little extra functionality to the built-in movement, and doing so ends up making it slower. All depends on what features you want.
I think Rush's last sentence basically sums it up. The only difference in most of the pixel movement libraries you see is exactly what kind of functionality they have. Some add things like movement easing, sliding, bouncing, ect. Others add stuff like omni-directional movement, allowing completely free movement on a 2D plane, not restricted to 8 directions. Other, less well-written ones just circumvent BYOND's native pixel movement in lieu of their own "custom" movement system.

What exactly are you wanting to accomplish with pixel movement that BYOND's native design won't allow for?
any recommendations for a mmorpg with fast paced combat?
It entirely depends on the features you want. The built in pixel movement will do nearly everything you need, however certain things like pixel-perfect hitboxes will require some work. I'm not too sure there's a library out there that implements PP hitboxes, infact I should go write one, since it's fairly intensive (Most AAA games still use standard boxes, only a few specific games do that.

Things like ramps and diagonals are handled by FA's library fairly well, but it does other things badly.

It all depends on what you need, and it's not feasible to pick and choose. Unless you have exact specifics on what you want, I'd recommend using the built in pixel movement, and adding your own features as you need.
The best advice we can give you is to just use the default system until you find that you need to add new functionality to it, then just add it yourself, it's really easy.

Case and point is that it seems like you don't know much about pixel movement itself in the first place. Do some research, play with default pixel movement for a bit and get an understanding for what it actually is before worrying about trying to change it.