I'm surprised Danny hasn't chimed in yet, but I know he is a tube guy. He chose to power his demo LS6/9 at RMAF using custom Dodd monster 275 watt 'battleship' tube monoblocks which were $50,000 or so.
Living in the Denver area, I have attended the annual RMAF for a few years now, and have heard the both the LS6 and 9s powered by many different amp systems including the above plus Red Rock Renaissance tube(40 watts) and Channel Island SS 500 watt. To my ears, they all sounded great, although the Red Rock tubes didn't have enough juice to fully show off the dynamics the LSs are capable of.
My LS9s (three actually) are part of my dedicated home theater, and are powered by a 7 channel Gemstone Blue Diamond (200 watt/channel) with a Pass Labs X1 preamp for 2 channel bypass, and an Outlaw 950 prepro for surround sound (which is due for replacement). These are all solid state. The room is fully treated and was designed by Rives audio. I prefer the sound in my room.
The biggest difference in these various systems, in my opinion, is the room acoustics and speaker placement, not the amplification. So if you are a tube guy, go with tubes. If you like solid state, then go there.