If you post a photo of yourself it would help us decide. I can just tell you a little about them.
On the Streetfighter V4, you are obliged to ride mostly on one wheel, either is fine, and have attitude. Which makes me seriously question having bi-plane wings on a streetfighter, but I digress. You can be a nice person, however, while riding it's about fighting with other naked street bikes. You should only dress in black if you have a sword it's ok too. It's a little taller than the Monster, longer travel suspension, feels a little more open, arms wider on the bars etc. It has the ergonomics for large body movements. So sword fighting is good here.
The Monster's origins are the ugly frankenstein red-headed-step-child made of chopped up ex-race-bike parts that accidentally is one of the best all-around street bikes ever made. It does everything well, track, street, long trips, two-up, kicking around and canyon rides. (not a race bike though) The older 600 sizes were fun as hellz, the 1200's is a lot more of that. Now it's deeply evolved from "old race bike parts," but still has that thing that it is. I haven't ridden the latest but I rode a lot of them, & a lot of my friends have the newest ones; seems like it's still the thing it's always been. I'm glad they got over the "mass-customization" trend that was really stupid a few years ago which means you are obliged to customize it yourself to match your personality not just snap on new tank colors (PALM-TO-FACE wtf). And you better make it really good, outlandish, outrageous, beautiful, and don't let me catch you throwing on an extended swing-arm or we're going to have a talk afterwards, but almost everything else is ok if it's not just no-effort snap-on parts (says the guy with the 99% stock Panigale.) But that's the deal.
btw, the V4 is blowing everyone's mind (except the older luddite curmudgeons) it has arrived to another level of sophistication and ride-ability and that counts a lot when you're talking about clearing 200hp. The luddite argument tends to be everything should furiously burn rubber and if you high-side and die, that's the Darwin awards working well. The tech argument is, you can just turn all the electronics off when you want and test your delicate wrist action / wheelie for 700 meters in 5th no problem. The race bikes have an obsession with making all efforts moving the bike forward in the least amount of lap time possible, that's not your camp here, but that's what comes with the V4 as a hand-me-down.
So what do ya want? Raw grunting fun as hellz style or something confusing with bi-wings that goes lightspeed? I think either are going to make you spit you facesheild opaque with laughter every time you leave the last stop light in town. It's more about who you want to be (NOT who you were born, don't get confused). Are you ok with strapping on ballet gear for Tutu-Tuesday, or are you more of a tattooed with fashionable facial hair and / or piercings kind of a person?