By and large, the top bowlers in the world can use just about any brand and be successful; that's because they know how to read lanes, adjust to transition, and repeat quality shots.
Now, that being said, ball/company selection can still be very important in terms of matching up. Bowling is all about matchups. When you properly match ball type, drilling layout, ball surface and bowler style to the conditions, you will get good scores (provided the bowler can handle his or her end of the bargain). When you have bad matchups, you often get bad scores.
Take a guy like WRWJr. Walter has spent time on several different staffs, and he has been successful with pretty much all of them. Then you take guys like PDW (Storm/Roto) and PBIII (Brunswick) who have been with one company for a large part of their careers. Personally, I'm guessing either of those two guys could switch companies tomorrow and still be just fine; they are that good. However, they stay with what they know because they are treated well by the companies (theoretically anyway), and they feel confident that the balls from those companies have always matched up well for them. That confidence can go a long way.
Now, we have also seen other pros switch companies and then go into a funk. If I'm remembering correctly, Patrick Allen struggled after moving from Hammer to Track. Did that mean that Track balls were bad while Hammer is good? No. There could've been lots of factors. Maybe it was matchups, maybe it was injuries/off-the-lanes issues, and maybe it was just a lack of confidence after the move.
So, long story short, it's a bowler's individual decision. In the end, I don't think any of the mainstream manufacturers make bad balls. Your bigger companies, Storm, Ebonite, Brunswick, etc. tend to have more money to operate with, so sometimes they can do more R&D than the smaller brands. Still, I think you'd be hard-pressed to find "bad balls" out there. It's more bad matchups to the bowlers and conditions.