I think the Jem is a great all rounder, it's a 100% rock machine but it can be used effectively in several other situations.
I've used my 7VWH for the following gigs/projects:
Samba (with big honkin drum section)
Jazz (cigar smoke & goatees)
Country (& Western, both types...)
Funk & Rn'B(get on that middle pickup in a clean channel and a wah and I can't be stopped)
Folky singer/songwritery stuff
Blues (playing slide and using the trem at the same time turns some heads)
Some traditional Chinese music
Celtic (doubling mandolin parts)
There's not a lot you can't use a Jem for, but then again, you can say that of most Strat hybrids.
With an acoustic bridge and a coil tap you'd be able to do just about anything with it.
If I use another guitar such as an SG for something it's usually more for the tactile change.
I can see a BSB getting funny looks in some situations but the 7VWH is classy/cheesy enough to look cool most of the time. I'd love to see a SK or a PMC in a bluegrass band!!
I keep my 7VWH next to me at all times in the studio, it's the first thing I reach for.