I like the three-faction division in Fading Shadows version of Ankh-Theb. It reminds me of the feel of Scars of Mirrodin, with G/B phyrexians, R/W mirrans, and U as a third party. For Ankh-Theb, though, I think we still need a better understanding of the factions' gameplay, as well as how the other color combinations might play in draft.
W/B - Religious, temple-building society, with many servants toiling to support an upper class.
Play style: tokens and ways to make use of them for the benefit of a few (like convoke, sacrifice effects, afterlife, eating the dead, i.e. Vile Rebirth)
G/U - Farming, river society, cyclic growth with the seasons.
Play style: cyclic gameplay, with big turns followed by lean turns. "Growing" mechanics like the thallids, spells that get better if you've cast another spell (i.e., Dream Thief from morningtide).
R - Nomadic, desert tribes.
Play style: Not sure. Maybe saboteur abilities? I don't particularly like the Viashino Sandscout mechanic.
Archtypes:
UR - Tempo deck: bounce, burn, and saboteurs
BG - ?
RW - tokens and pump
WU - ?
UB - ?
BR - ?
RG - ?
GW - ?