A quick point about setting for this fight. I'm giving the fighters no prep time and I'm placing it in Piltover, so city environment with cover. fighters start at just out of Vi's vault breaker range.
The last time these two fought was when Jinx ran Vi around the Piltover Bank and Vi smashed it to pieces. However this was planned by Jinx who probably knew the lay out well. This put Vi at a severe disadvantage. On the other hand Jinx in that fight was basically toying with Vi and didn't have intentions to kill her, just make fun of her.
This fight really comes down to "Can Vi land a hit?" Because those fists should mean lights out for practically anyone especially someone as skinny as jinx. Even if Jinx is strong enough to carry fish-bones and pow-pow, I don't think it helps her endurance taking a hit, her upper body may be great, but she lacks in the bulk department. If Vi can get in to range to deliver her denting blows then Jinx loses handily. Jinx basically needs to cut through armor with her mini guns and rocket launcher. For the sake of this not being a moot point I'm going to assume hextech technology is good enough to be able to generally be able to block bullets so Vi would be able to block pow-pow with her gauntlets and armor. however Jinx's Zap and flame chompers will make life hell for Vi.
There is also an argument to be made about temperament. If Jinx got the drop on Vi she probably wouldn't take her out instantly, instead preferring to make fun of her and embarrass her first. Vi on the other hand would certainly be willing to crush jinx given the opportunity. So there might be a bit of over-confidence on Jinx's part could play into Vi's favor.
Overall I give this to Vi. She's generally built for pursuing and her hextech equipment should be able to keep her alive long enough to be in close range. Since the fight most likely would take place in Piltover rather than SR I think that she could also utilize cover. I'm not giving the two any prep time here so Jinx would have to rely on the chompers she brought with her and I don't think that would be enough to stop Vi's charge. I do think this is a close fight, guns are powerful and with the right positioning Jinx could easily pin Vi down into an environmental trap or something else to give her the edge, but I feel her over-confidence and need to make fun of Vi will keep her from fighting as smart as she should.
One final note on the Super Mega Death Rocket. I didn't really consider that in this fight, because I think it would be powerful enough to level a large building and in the case of this fight it would probably end up killing them both before anything else.
Therefore I think that the winner is 
60:40 
vs 
Verses Zilean
