The silicone pieces that I have are not felted, they are just bare. My silicone pieces stick on a vinyl board just like felted pieces stick on a silicone board. But I'd say not really any worse and no worse when playing with silicone pieces on my silicone board. You won't be sliding your pieces, but your knight will survive when a rook knocks it off the board. Is that my favorite set to play with? Not by a long shot. Is it a superior way to deal with blitz play and especially kids or adults who slam their pieces like kids? For some people, yes.
Recommendations for a Speed Chess Set?

Pieces:
HoS Fischer Series 3.75"
The color would be your choice
http://www.houseofstaunton.com/the-fischer-series-plastic-chessmen-4-0-king-13238.html
Board:
Silicone Board is nice, vinyl is fine, Mousepad don't get it
Many sources online
Clock:
If Z-Mart II's touch sensors are not for you, get a DGT Easy Plus or NA

I'm surprised no one mentioned Bobby Fischer Ultimates in plastic. Very durable and heavily weighted. They shouldn't tip in bullet or blitz games.
Although not weighted, silicone pieces are the most durable.
What specific time controls? DGT 1001/1002 are very inexpensive and might have the time control you want. I don't think they'd survive a far fall though.
They also make silicone chess pieces. Aesthetically perhaps not what one would hope, but durable as all get out. I have a set that I bought from USCF, but I haven't really played with them.
Our club has a couple sets of these--the kids call them "rubber" and love to throw them! They are not too rubbery, you don't really notice until you try bending them, and so far being thrown by kids has not damaged them at all.
(Seattle is notable for very strong young chessplayers; they are serious over the board, but the skittles room regularly gets trashed.)
haha, I bet skittles rooms around the country get trashed on a weekly basis! Question, do the silicone sets have different material on the bottom? I'd imagine silicone piece on silicone board would stick like glue.