Another possible advantage of the 3-spool over the 2-spool is physical size. Having flown B777 with GE90-76B and -85B engines, and also RR Trent 895 engines, the triple-spool Trent has significantly less diameter around the engine cowling than the GE (around 24 inches less!). This gives greater ground clearance below the Trent, when compared to a GE hanging on the same aircraft type. Not of huge significance on the B777, I know, but it may be on other aircraft where ground clearnce is more critical?
I guess the already-mentioned efficiency (running closer to optimum RPM) of the 3-spools allows reduced fan diameter. In the case of the Trent 895, it also produces more thrust than both marks of the GE90 mentioned, but still has slightly better fuel economy (3-spool efficiency again?).