IMO, the LCD-2 and 3 are voiced (much) differently. The 2 can sound "dark" compared to the 3, which can sound generally warmer. The 3's treble can sometimes sound rolled off, whereas the 2's have a tendency to have more treble response.
The fazored 3's seem to have a halo of added bass and treble in comparison with the classic 3's... I'm not sure if this is true of the 2 classic vs fazored.
I would strongly recommend trying the pair of headphones you end up buying, and doing a direct comparison. There is so much variance between different pairs and drivers, it's hard to say which you'd prefer, and if you would hear the same sound from different pairs of headphones. I preferred the LCD-3C's that EdmontonCanuck had to my LCD-3F's... I also preferred a pair of LCD 2.1's to 2.2's that I heard as well. IMO, there is much variance between different LCD headphones... it really depends on the FR of the drivers, and your personal taste.