Just show me the fastest.
The fastest, hmm... Is Fridrich, Petrus or Roux the fastest for speedcubing?
Fridrich:
1. Theoretically slower in terms of move count.
2. Practically faster because of near-zero pauses throughout the solve.
3. The fastest way to get fast, requires relatively less practice vis-a-vis Petrus/Roux.
Petrus/Roux:
1. Theoretically faster in terms of move count.
2. Practically slower because of thinking time.
3. Takes relatively more practice to get fast.
You be the judge.
In big cubes BLD, Petrus/Roux is equivalent to full commutators for corners, edges and centers; Fridrich, on the other hand, is equivalent to "all the other methods" i.e. 3OP corners, Old Pochmann corners, R2 corners, r2 edges, r2 centers (this is all I know, let me know if there are more).
The difference between speedcubing and big cubes BLD is in big cubes BLD, the fastest guys use full commutators (equivalent to Petrus/Roux). If you think it's gonna cost you a lotta time and effort to get there (like I do), then go for the faster ways to get fast ("the other methods"). Does this answer your question? (Edit: if you wanna know why the commutator guys are faster than the "other methods" guys, it's because the "other methods" guys haven't reached the non-stop zero-thinking execution nirvana yet, whereas the commutator guys have, so commutators are currently faster both in theory and in practice.)
For edge commutators, try Chris' guides in the how-to section. Link:
http://www.speedsolving.com/forum/showthread.php?t=201.
For center commutators, I recommend Mike's guide at
http://www.speedsolving.com/forum/showthread.php?t=2207. (I didn't learn it there, I figured it out on my own, but I've read it and it's very similar to the way I think of commutators, so I like it.)
For the general underlying principles of commutators, which is gonna be very helpful when you try cubes bigger then the 4x4x4 and don't feel like learning more commutators, read this:
http://www.speedsolving.com/forum/showthread.php?t=697. I like it because it's the universal laws of commutators and applies to any and every situation so you can always come back to these principles when you get stuck. Only thing that you might not be comfortable with (though I am), is that it's all pure theory, and I think a few examples.
For r2, try Erik's page for a little explanation and Lucas' page for more algorithms.
Erik:
http://erikku.er.funpic.org/rubik/r2.html
Lucas:
http://cube.garron.us/BLD/r2/index.htm
For R2, Old Pochmann and 3OP corners, I'm pretty sure you know where to find resources if you've come as far as 4x4x4 BLD.
I know it seems stupid that I've provided almost every resource available for 4x4x4 BLD, but I don't want you to miss out on anything because I think they're all helpful in one way or another, so I've tried my best to provide a short description for every link so you know what you want to read first, and what you want to leave towards the end when you're more familiar with the basic stuff. Yeah.