I guess it's what papers you can get. AES will (I think) issue pink papers for an approved stallion from any studbook and mare does not have to be graded.
BWBS (again I think) may only offer pink papers to stallions and mares graded in their own studbook and it may be white papers if mare or stallion not graded with them.
I stand to be corrected though as this is all quite new to me at the moment. Best is to phone up and see what they can offer you.
The grey in my sig is currently registered SHB(GB) however, she is eligible for BWBS pink papers as both stallion and mare were registered BWBS. However, as she wasn't originally registered with them, I have to take her to a grading later this year. I wouldn't have bothered with the grading but I want to breed from her in the next couple of years (and want to use a BWBS stallion) so I'd rather get it done before she's put in foal.