If you rule out the newer generation 1000cc bike, the Older and newer 650cc bikes had a noticeable weight advantage over the older 1000cc.
Yes the 1000 has more poke if your talking standing quarter mile, but in the twisties the 650 is more nimble where the 1000cc can't use all that grunt and you have too throw the extra weight around.
I had a Wee for 60k miles, loved it. Did loads of touring 2up, very over loaded and It never complained. The rear shock needed a spring upgrade which transformed the bike for touring, but the same saggy rear end is a complaint for many for the 1000 also.
I the real world the 650 is the better bike, that didn't stop me looking for a Vee when my Wee died, but If I'd found a good one of each for the right price it would have been a very hard decision to choose one from the other.
I went looking mainly for a Vee as I'd had a Wee as my first big bike, put loads of miles on it, but at the age of 30 having a bigger bike was something I felt I should try. That and we were doing a fair bit of touring 2up and a bit of extra grunt will make for more relaxed cruising.
End of the day I didn't find a good condition Strom for the right price, so I became a traitor and bought an 'onda Varadero. Most of the 650cc bikes from other manufacturers either didn't quite meet my needs or made me physically sick when looking at them (Versys and later Transpalp 700).
At the end of the day it's your choice, we can only give you our opinions.
I truly miss the nimbleness and free revving nature of the my K6 Wee. The Varadero is a fat old girl and nowhere as nimble as the 650cc Strom. There is a fair chance my next bike will be another 650cc V-Strom.
(I ruled out the new 1000cc bike as it's USD forks, Radial brakes, traction control, slipper clutch and various other bits make it significantly different from the older Vee and Wee/Glees)