Joe uses Scratch Live, he's been using that on stage since MTM came out. It allows him to store all his scratch samples on his laptop in the Scratch Live program, bank up/down from sample to sample during the set and use the Scratch Live control record to scratch them, which is a lot easier than having to switch vinyls all the time.
LP creates all of their samples themselves and loads them into their samplers. The M-Audio pads that they've been using since MTM came out don't even come with any samples on them, I'm pretty sure.
Rob uses the same kind of samplers that Joe does, he has 5 triggers on his drumset (the 3 Pintech pads, a digital kick pedal next to his regular bass drum pedal, and a trigger on his snare drum) that each have different samples routed to them. I think his sampler might actually be part of Joe's rig and Joe switches the samples for him, I've never seen a sampler anywhere around his drum kit.