I guess it depends. I'm a very divergent thinker. I like hearing about research done by others, and enjoying thinking of new ideas for them just for fun. It's a strength, but only if focused properly. I'm not arrogant enough to think I'll make a career out of doing research on "everything", so even though I'd probably feel better with a lax mentor, I'd probably do better and learn more with one who's more structured. My current (undergrad) adviser is like that, and I'm lucky enough that I'll have two in grad school who will be the same. Of course, in this case, it's even more critical that I identify strongly with my mentor's research. Luckily, I do. Just my two cents.