There aren't any big disadvantages to running 15 inch wheels other than the possibility of grinding your calipers to fit them. It seems like people have a pretty good success rate with NOT needing to grind calipers with Soft 8 style wheels. Personally, I'm running 15x8 Unique 297 wheels and didn't have to grind calipers. I guess the only other thing is if you air down too low on some tires, you'll get a "folding" action when crawling instead of the tire wrapping around rocks. Otherwise 35s on 15s is a very common setup.
One thing to note is that there aren't any 37 inch tires out there for 15s so 35 is the biggest you can go. I'm sure someone will find some random brand and model that's offered in 37s but you can't find popular brands in that size. Also, if you ever want to do a brake upgrade, there's no room.
'09 X Unlimited, 4WD, auto, half-doors, soft-top
RC 2.5" Series II BB, JKS Quick Discos, JKS adjustable front track bar
15x8 Unique 297 (Soft 8), Goodyear MTR/Kevlar 35x12.50R15
5.13 gears, ARB front locker, Currie front shafts
Bushwacker flat flares, Rubicon rails with steps added