I didn't know that GECAS was bigger than ILFC!
Actually, I believe that many of Europe's airlines fly fleets of A319/A320/A321 planes all leased from either GECAS or ILFC. Mostly because (I think) many European airlines can't afford to buy the plane for the long term and would rather get the plane on a lease. Given that CFM International engines power the majority of the A319/A320/A321 fleet and the A340's, GECAS must be able to wring out a pretty good deal on things like engine services. GECAS must be doing land office business with Inclusive Tour (IT) operators in Europe, since these companies almost by rule lease their planes.
In fact, I can almost say that when NW orders their replacement for the D10 fleet (e.g., either the 764 or A333), they might just do it through a GECAS long-term lease.