I lusted over the Monster for the longest time, it really was a stunning bike and a buddy convinced me that if that is the type of bike I really wanted, skip right over it for an SV650. Even if I perform the maintenance I am still on the hook for parts.
Neither the Monster or the SV fit the "adventure bike" profile the OP described as wanting. Not that either bike would not be fun as hell but probably not on the dirt although there is a Ducati Scrambler.
I have not ridden, only looked at and sat on the V-Strom I agree with the suggestion.
