I have no first hand experience with them, but know a little about them. You looking at the 650 or the 1k? FWIW, the Strom is pretty much a cousin to the SV.
Their engines are based on the SV series, with different cams, compression ratios, and possibly different heads (but unsure on that one). The are "de-tuned" for more midrange toruqe, which usually means "de-tuned for less power everywhere".
They're a great bike for long distance touring, and decent at LIGHT offroad use (dirt/gravel roads, but not really made for the mud like a real dual sport is). Windshields are adjustable (3 position i believe).
On road handling in the twisties is decent. The SV handles better, but the V-Strom isn't really as "twisty based" as the SV either. If you're looking for sportbike handling, look at a different bike.
Much like BMW's, they have love it or hate it looks. A couple different mags have in fact called them the "poor mans bimmer". Sine you like BMW's, I'm guessing you love the Strom.
The ONLY complaint I've heard/read about them is the wind noise from the windshield no matter what position you put it in. Problem easily cured by an aftermarket windshield.
Top speed on the 650 is around 105-110, and the 1k tops out around 135 (remember, they're "de-tuned"). Roughly 20mph slower than the SV counterpart.
All the above info was stuff I either read in a magazine, or read from a review a owner posted up somewhere.
Edit: My OPINION on them is they're ugly as shit, but are likely bullet proof. Engine has been proven for years. 7 years on the 650, and like, 10 or so on the 1k (Strom 1k is based on the SV1k which is LOOSELY based on the TL1k engine).