Which method is the best for 3x3?

Other methods:
Roux
ZZ
Petrus

Use google to find resources for them, or other threads similar to this.
There is no best method, just one that works best for you. People have got sub-6 with both CFOP and Roux.
 
you're using the right method to get faster, just keep practicing and you'll improve heaps.
Also it's probably better to learn full PLL first before COLL.
 
First off, define "advanced cross."
Second, your F2L should at least be sub-15 seconds before you even think about moving on to a 2 or 3LLL last layer. It would be more beneficial to improve your F2L.
Third, COLL is a waste of time unless you know 2LLL, and if you meant 1L OLL, then PLL is easier to learn and will save more time. If anything, just learn the 8 no edges oriented 1L OLL algs and you'll be fine.

Just practice your F2L a lot, with strategies such as a metronome, putting in the pair blindfolded, and maybe learning some advanced F2L tricks. And for the cross, plot the whole thing out in inspection. The W.H.O.L.E. thing.
 
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