I guess at this site we’re looking primarily at bluegrass players.  I don’t know what best means either, but some of my favorites:
Mandolin:  Joe Walsh and Tim O’Brien.  Sam Bush and Sarah Jarosch are in the mix too.  I actually don’t care much for Thile.   I don’t know why, I guess I like to imagine myself playing the stuff that the guys I listen to play, and with Thile that’s too much of a stretch. But also, he’s just too busy, if a phrase needs 2 notes he’ll play 55. I like it less cluttered.
Fiddle:  Michael Cleveland is awesome.  First time I saw him up our way, I didn’t even realize he was blind.  I also dig Stuart Duncan and Alison Krause.
Guitar:  Stormin’ Norman. And of course, The Man.  I never did get the chance to see Tony live, and it doesn’t sound like I ever will. Sniff.
Dobro:  Jerry Douglas,  Cindy Cashdollar although I’m not sure how BG she is considered.
Bass:  I don’t know, they all sound good, and the same to my ears.  The bass player in my band would have my head if he heard me say that.
Banjo:  Uh, no.  Thanks for asking. 