Technically speaking, the quartersawn maple is a bit stronger against flexing. But not realistically/practically very much more when considering the neck as a whole. And I wouldn't say that it is more "stable". Like Fender, I have been using flat sawn maple necks since I have been making guitars. I haven't noticed any flex in my necks. But all of them have a laminated center strip (of at least three pieces of very hard wood), a separate laminated hardwood fret board, and a truss rod. In my opinion, flat sawn is much more aesthetic. So, with the better aesthetics and the engineered strength, it's a no-brainer to me.
I can't think of any negative aspects to quartersawn maple other than the aesthetics, but I've also seen some mighty pretty grain in some quartersawn necks.
You pick. I don't think you can go wrong with either.