I am not really qualified to comment on the GF as I only own a BM, but I will anyway. As I see it the major advantage is the controller on the BM which is pretty much set and forget after dough in to the point of removing the malt pipe prior to the boil, while with the GF you need to manually enter each step after the completion of the last.
One thing I prefer on the GF though, is the top down flow of wort through the grain bed. This has the advantage filtering the fine particles effectively which stay at the top of the grain bed when the malt pipe is removed. On the BM, the fines are trapped at the bottom of the malt pipe and alot seems to fall back into the wort as soon as the malt pipe is removed. The result is you end up boiling cloudy wort.
Flamesuit on because I know that what is important is the clarity of the wort to the fermenter, not so much the boiler, but I'd still rather be boiling clarified wort which to me is part of what a RIMS system should achieve.