As above, If you are a big bloke go the Vee, If you are not the Wee.
The Vee covers a lot of ground really well but is a bit more of a handful in the dirt so that limits the knarlyness that is available, but it would be quite capable of towing a small DAK DAK, two up with luggage and a 20litre drum of fuel
If you are mainly on your own the only real advantage on the Vee, apart from the grunt, is the better front suspenders.
Engine is sweeter on the Wee and would be amazing after the KLR. The Vee really feels like you have two thumpers in the bike at legal highway speeds. (3K-4K RPM)
Regards the top heavy nature.
This has a bit to do with having 25Kg (or whatever they are, they are heavy bastards) of standard muflers up high, not so much the increase in engine weight, which is right down low.
My bike with staintunes installed has been measured at 205Kg Wet with 1/2 tank of fuel and GIVI crash bars.
So the aftermarket exhaust also saves a fair amount of high up weight and they sound better if that is your thing. I run them baffles in. That is about as much noise as I need on a long trip.