Hello.
I would consider myself still pretty much a beginner speedcuber who's open to the idea of learning a different method (barely sub-1:00 on 3x3 with CFOP and not particularly attached to it). After reading the guide and skimming through the rest of this thread, there's one thing which was only briefly touched on, which is the 3x3 stage on bigger cubes.
From what I gather, Roux is out of the question because of all the M moves, and most people use CFOP. But what would be the pros and cons of CFOP vs. ZZ or Petrus for this purpose? Or does it really matter?
Is "effectiveness for 3x3 stage on big cubes" a crucial factor to consider for someone who would like to become a decent all-around speedcuber, or is it not that big of a deal?
Roux is actually still good on 4x4. It's 5x5+ where it's not a good method to use.
CFOP is a very good method for bigcubes. It doesn't rely on inspection very much and there are several methods which have the cross solved before you reach the 3x3 stage, which can help save time.
ZZ is okay, but not great. It relies a bit more on inspection, but for a good ZZ user this shouldn't be too much of an issue. If you can see OLL parity in inspection you can probably do a faster OLL parity alg than most other people, since you don't need to preserve permutation before solving anything. Being able to do COLL every time is another benefit; EPLLs make PLL parity easier to see, and are easier to do on bigcubes because they're <R, U>. However... some people find the <L, U, R> F2L harder to do quickly on bigcubes, and this can cause lockups.
Petrus isn't as good a method for 3x3 anyway, and it's not too good on bigcubes either, unless you're using a method where an XX-cross (maybe without the last edge) is solved by the 3x3 stage, like OBLBL or Yau5/Hoya5. This is because it relies on inspection; you need to be colour neutral to be able to use Petrus' blockbuilding efficiency as much as possible. Being CN is a bit impractical for the 3x3 stage of reduction since you don't have time to check all the blocks. However, after the blocks are built it's good, since you can orient edges easily and again could possibly use an easier OLL parity alg. The LL is nice, same as ZZ, because you can either do COLL or OCLL.
But really, the 3x3 stage isn't a big part of the solve at all, especially on bigger bigcubes. The reduction part is far more important. 3x3 is only really important in 4x4.