Maybe that's because it's a Flying V with different body/specs than a Les Paul.
With 'dark' I mean low middy instead of high middy.
True, of course - and it's a
very lightweight V as well, which probably plays a part.
And I was thinking about the low mids too - that's what I've always read about the BD, but it doesn't seem to come through much in the V. I might try the BD in another guitar some time and get a Riff Raff for the V (which is brighter again of course, but I think it'd suit the V and go well with the SM neck).
That's just given me an idea...