| Last year a friend of mine bought both the shuttle and the LMII so we spend many afternoons messing around with them doing the A/B thing, with electric and acoustic basses.
With electric, I was partial to the transparency of the LMII since I like the sound of my 4,000 dollar custom bass to shine through, uncolored. But that vintage emulation knob can really add some awesome old skill grit and the midrange scoop knob is nice, so the amp really has a couple different personalities. Granted, they both are seriously awesome. My friend found the GB to more to his liking, because the GB tube preamp had been an element of his electric tone for a year or so, in his larger rig, before he got the shuttle.
On the double, it was a close call because both are extremely versatile. I haven't found and amp yet that doesn't require some serious EQing to get a respectable tone with only a DB pickup, so both will give you a lot of eq options to try and optimize your amp sound for the particular room you're in.
It's crazy how a lame, bottomless amp sound can actually sound great from across a boomy room.
I'd try both if you can, but I really don't think you can go wrong with either if you're looking for a ultra lightweight head.
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Yeah, I double...don't you? | 
