Are you referring to this one?
Or this one?
How would this compare to the Little Dot MK III?
I haven't heard the Little Dot MKIII, I have read good things about it, FWIR the Rock & Glass has nicer parts (and a simpler circuit) than the Little Dot I+ and the MKII, but I don't know how it directly compares to the MKIII. Personally though I just have really been enjoying the Rock & glass since I got it, it's cheaper to only have to roll one tube at a time and the amp looks quite handsome. The Rock & Glass sure sounds like a $220 amp, though you'd probably be fine with either.
You can find tubes that warm or even thicken up the sound, but so far I have just been super pleased with the liquid midrange and clean bass and treble from putting a Sylvania JAN 6DJ8 tube in it, commonly and cheaply available on eBay. The amp itself doesn't distort bass into sounding boomy-er... Say, for example, you're used to dubstep in a car going WUUB WUUB buhDA! on the edge of loosing control and you feel it thump your chest and squirm your stomach and it's a little scary and fun. Well, you probably already know using the Q701 you won't have that feeling of your guts resonating, but with a decent amp you'll hear Vraub Vrub duh-PAh!, sound pressure impact on leading edge but a quick controlled decay that reveals the timbre and detail of the notes, and with the tube amp you'll still hear that and (IMO) a kind of euphoric cohesion because the presentation is just a bit less dry.