we play ren often because it is most (but still not completely) balanced civ wise - in ren starts u can have units from classical to industrial era, and most of civs have something (uu or ub) in that period, greece is not overpowered but still have somehting (well cheap 5 move unit with 14 str at early start is still neat) - only overpowered civ is france, but that for all eras.
Also ren have much wider policy choice, and 4-5 trees are viable for choosing depending on map-civ-start loc.
Medieval start have greece terribly overpowered, france even more so, and civ balance is not so smooth like in ren.
But medi is good if no greece.