I crossed two GAI cards to SGC (quite awhile back), one graded same and one got a bump up one grade. I sent them to SGC still in the GAI holders, but they were the older GAI holders. After that, I read a lot of things that made me a bit uncomfortable buying GAI graded cards, so now I stick to the others (SGC,BVG,PSA)~or raw
I guess it's a gamble- it's probably best to know the type of card you are buying in the holder, and be able to somewhat tell if the card & grade look right to you before pulling the trigger.
Good luck
Sincerely, Clayton