The only major columns-first cuber that I know of is Akimoto--

his overview of the solution is

here.

my method uses his as a starting point, then...changes some stuff. (first part and last part are different)

essentially, you first get the columns (akimoto does four white corners followed by insterting edge pairs...I instead match edge pairs, then do an F2L-like thing...), then you do white center pieces, followed by 3 pairs of white edges, then all other centers (using the free white edge pair), then complete the final white edge pair, then dooo last layer.

it's quite fun to do, actually. works on 5x5x5 kinda but it's...ugly. or maybe i just dont know enough to apply it there.

in any case, centers first -seems- like it's in general faster, looking at all the fastest times on speedcubing.com. however, you can't really make that good of a judgement because no one really uses columns first. except akimoto, and he got an average of 1:18.96, which is....pretty great. so i know the method has potential.

i dont know exactly how to get there though...there's not much documentation...watching akimoto's solving vids helped.

right now i'm struggling around the 2 min barrier. used to be able to break 2 mins fairly often but then i started experimenting with other things so i need to figure it all out.

for last layer (i use some of these for inserting the 4th edge pair too), i use 8 different algs, which are all based on RUR'U'rR'URU'r'...

1) RUR'U'rR'URU'r'

2) inverse of #1

3) R'U'RUr'RU'R'Ur ("reverse" of #1)

4) inverse of #3

5) RUR'U'RwwRw'URU'Rww'RwR' (this notation sucks but i dont really know how else to describe it accurately--its basically #1, but...moving a different slice)

6) inverse of #6

7) R'U'RURww'RwU'R'URwwRw'R ("reverse" of #5)

8) inverse of #7

so i use those, plus set-up moves if necessary.

in most cases I can pair up one pair of last layer edges while inserting the last white edge pair. then i usually do COLL->3x3x3 edge permute->1 or 2 of the above algs->fix parity if necessary.