Tire fit from different manufacturers is akin to clothing fit from different manufacturers. They'll all have the same BSD, but some might have a little more below (inside?) that than others.
Stiffer rubber compounds make the job a little harder, supple rubber is a little easier. Gatorskins obviously come from the former group, and you might need to resort to judicious use of steel core levers to pop that bead in place. +1 to thinner rim tape, since that extra mm of depth can make the difference between needing a lever or not. I swapped the front tire this morning for a more supple compound over the Michelin ProTek I bought for better control on Mackinac Island's unpaved road segments. I only recently realized that the cheapie Forte Urban II tires that were on the bike when I bought it are 1) lighter; and 2) more supple.