Yes, that notation is more common, but the problem is that it doesn't scale well for NxNxN cubes. It fixes the centers for 3x3x3 cubes, and it doesn't handle the inner slices for 4x4x4 or higher order cubes. The notation I described was reasonably compact, and handled cubes up to 9x9x9. That's why I went with it.
The security really gets worse the larger the cube -- mainly because of key-length. True, the total number of permutations goes up exponentially (and how! one -factor- in the number of permutations is 24!floor((N-1)/2). I don't have time to compute the other factors, but with that exponential base, who cares?), but the number of permutations that can be reached within m quarter-turns is less than 12Nm. If you want to reach anywhere near a decent subset of the permutations, you are going to quickly need huge keys. If you use too small of keys, you get too little mixing, which ruins your cipher. I'd be interested to know when the length of good keys exceeds the length of the datablock (6N2). I suspect it happens quite low -- I know 3x3x3 cubes require at least 22 quarter-turns to reach all permutations, with a datablock size of 24 characters.