|First off, like with anything else, there's no right or wrong. Just different styles for different people. But I find that it helps reading about the paths that others chose, the hassles they had to deal with while on 'em and the rewards they gained in the end.|
So, as far as slide and bottleneck playing goes I find that each technique poses specific advantages.
Fingerpicks will give you speed. If your style is closer to bluegrass or country than blues, fingerpicks are a must. It's almost impossible to get your right hand flying as fast with any other sort of equipment. If you're playing a lap guithar, fingerpicks will come in handy also, regardless of style, because otherwise your wrist may suffer. The downside: In any style other than country or Hawaian your sliding will sound a bit awkward, with a sort of a tin can quality to it. Bob Brozman will play his Nationals with fingerpicks only. I consider him a musical genious, however, not due to his slidework because of this fingerpick sound it comes with.
A flatpick's most obvious advantage for most players will be the compromise it offers. You're able to get some descent slide sounds out of it, while you're still holding what is arguably the most popular right hand companion for guitar players around the world to get you through the rest of the song / gig. Rock / electric players seem to go for flatpicks when they play slide 'cause it works best when the slide riffs aren't too complicated. The downside is you normally can't hit 2 or 3 strings simultaneously if they're not sequential. Of course there is Roy Rogers who plays with a flatpick but his technique is actually a combo of the flatpick and his middle and ring fingers. But remember, Roy is Roy. I find his technique impossible to play, if you're feeling up to the task good luck.
This is my personal favorite for slide playing, though I do use fingerpicks and flatpicks for other styles. The main benefit here is the sound. Somehow when the flesh of finger touches the string it produces a warmer sound, even with heavily distorted electric. Control and muting works alot better for me but this may be subjective, I guess a banjo player would argue against this. The downside is with some acoustic setups you're not loud enough and your nails need to be a little longer than you would normally want. Ry Cooder is an all-fingers man.
Although I never played a thumbpick alone (without the fingerpicks that is), I believe it is a style best suited for things like acoustic / folk. The benefit is you get the warmth of the finger style playing and you can get some extra volume from the thumbpick when you hit the bass strings - which may be a great relief for some guitars / songs.
Feel free to comment or share any experiences you have with these different styles.