In fairness to the OP, I have to say I understand but for me it's hilarious to the least as for the 2 machines in question.
Vespa vs. GS Giant
A little scoot tire will not negotiate much in the way of ruts or soft mud,sand, loos gravel,etc., so not fair to the Vespa to ask that of it? OTOH, most GS bikes are used for "soccer mom" duty" and never go into much in the way of serious nastiness. Speaking from just the experience of living for many years on dirt & gravel roads in my native KS, a Vespa would not have gotten me to work or back home on many days of the year-PERIOD! And thats just talking basic transportation in the boonies, not riding there on purpose.
I vote for what you can afford & maybe thats a fun & useful dirt bike thats tagged and perhaps a scoot to go with it if you like.
"If I had my life to live over,I'd dare to make more mistakes next time...I'd relax,I'd limber up.I'd be sillier than this trip, take fewer things seriously, I would take more chances... take more trips...climb more mountains...swim more rivers...eat more ice cream." Jorge Luis Borges, at age 85