I've ridden both and like them equally. My buddy has the Strom and it's an incredible ride. Performance is very similar with either bike - so little difference that I think that the rider would make a lot more difference on a curvy road than the choice of bike would. The Versys seems to be a little quicker handling, and may be since it has a much shorter wheelbase. The longer wheelbase of the Strom though, makes it much better for two-up riding and the slab. The Strom comes with a 19" front wheel, which makes it a bit better on rough dirt roads, but it also slows the handling slightly (very slightly) on the tarmac. The Strom is quieter with stock exhaust and as mentioned earlier, the stock seat is much more comfortable that the board on the Vee, but that's easily and cheaply remedied.
In cold weather, my buddie's Strom is a lot more comfortable than my Vee. He has handguards and a Cee Bailey windscreen and you feel like you're really protected from the elements when the temps drop. I've also got the VStrom handguards and Cee Bailey windscreen on the Vee and it's really helped, but it still doesn't protect me as well as on his bike.
The Strom looks as though it's a lot heavier and bulkier, but once underway, it handles every bit as easily as the Vee. The Vee is a wheelie treat - roll-on 'happy hops' are really easy in first gear and by shifting weight to the rear in second gear, longer sky grabs are easy and controllable.
Now the next one is strictly a personal observation, and not based so much on actual experience as simply a feeling that I have about the two bikes. There is something about the Strom that gives you the feeling that it's 'carved from stone', while to me at least, the Vee feels a bit more like the Ninja that was my last ride. It's good, it's really fun, but if I had to choose between the two bikes for an around the world ride, I'd go for the Strom. Maybe it's just because Suzuki has had more time to work out all of the bugs, but man, that bike feels solid.
Hands down though, I think that those two bikes are the best bargains on the market today. You won't go wrong with either one. Both have a huge variety of after market goodies available, a wide-spread dealer network, and they both sport engines that have been around for years and that have a terrific rep for reliability. Both bikes have forums dedicated to them, and both forums provide a well-informed and helpful community of riders. I'm even thinking about picking up a used Strom to back up my Vee as a 'project' bike.
One more little thing - I really do like the looks of both bikes - there is something really appealing to me in the looks of a bike that will do damned near everything but cook my dinner for me.