Thanks for the comments.
Norton1 is partially correct. I do play that style but also can play bare fingered as well as using metal picks on index and middle. (Currently I'm liking Kyser metal picks and an Ernie Ball thumbpick.) Most of the recordings that Menphis Mud referred to were in fact done using fingerpicks, and the reason is clarity, articulation and punch. There was one tune on that page which was done with just a thumbpick and bare fingers ("That'll Never Happen No More") - but the rest I think used metal picks, and I hate the sound of the clanging of the picks on the strings too. I've tried curving the ends of the metal picks so that the angle of attack limits the sliding of the picks on the strings. But like others have pointed out, with the digital technologies available today and the increased clarity of recordings you hear everything. In a perfect world, I'd use just a thumbpick and go bare fingered with a bit of nail for the attack. But more and more I'm getting into tunes with single string runs, breaks, and the whole two fingered flatpicking thing (ala Fred Henderson, Rev. Gary Davis, etc.) and for that, you need finger picks to get that bite and attack - or you'd shred your nails no matter how hard they might be. There is indeed a difference in angle of attack between playing with metal picks, or just using a thumb pick and fingers, or entirely bare fingered. It's really just a matter of practise and developing the muscle memory and realigning your hand to the new "grid" or arc. Metal picks require a higher arc and the others, not as much. Course it all changes again when you start using a muting or dampening effect on the bass strings and for that style of (Travis) playing again you need a thumb pick to get a good thud or whomp on the dampened strings.

Doesn't take long to adapt to any of them. The key is to just do it, and don't think about it too much. Your fingers will comply. In one of the first lessons I ever had with Rick (and I'd been using metal picks pretty extensively prior) was him telling me to remove the picks from index and middle and just play with a thumb pick. At first it felt really weird and all I heard was the bass from the thumbpick so much louder than the bare fingers. Within an hour of playing like this with him, the overall volume evened out, and the bare fingers started compensating and playing a bit harder. Just think of learning to play these various ways, as akin to learning how to ride a bicylce. Once you figure it out (and really it doesn't take that long) you'll be able to adapt more quickly in the long haul and the balance will find and right itself.