The real ruler is the Bearded Lady..
All hail the Bearded Lady!
the charming pirate miss fortune.
Who conspired to blow up GP's ship, set Bilgewater against itself, and played everyone for fools. Just to get revenge on GP. What makes you think she isn't just as ruthless as GP?
Does everywhere need a ruler? Gangplank as ruler may have been fine though a civilization without a ruler (for once) also sounds acceptable.
LoL has more than just Humans and Yordles, too. Interested parties may want to infiltrate and annex Bilgewater if not completely consume it Shadow Isle style.
Who we really need to rule is 
I don't feel like It's MF or GP.
she wants revenge for what Gangplank did and to purify Bilgewater, not to lead it. I can really relate to her story personally and just the character overall, but I don't feel like she should or even necessarily wants to rule over Bilgewater. She just wants to cleanse it and enjoy life again after getting revenge.
doesn't seem like he really cares for Bilgewater, just about maintaining his power. Maybe if he gave some of his gold to Bilgewater to construct it or something, but it feels like he just selfishly uses all of his gold for himself or his crew. He was sort of able to keep the place politically intact, though clearly doesn't care enough to make it a better place.
I think any of the two would be a fine ruler, by Bilgewater's standards... The only thing that brought chaos in the city was their struggle for power. Whomever were to succeed would be fine. As long as it doesn't have a nemesis trying to kill Him/Her and stealing His/Her power
Well, MF isn't really fighting to rule Bilgewater, unless she has intentions we aren't aware of. She completely destroyed the city just to get revenge on one man.
Meanwhile GP never acted ruthless for no reason. It was either to make him look more powerful, and thus keep the peace, or to save face by attacking someone who had wronged him, in order to keep the peace.
In terms of 'better ruler' Gangplank takes the cake by FAR.
should be the real answer.
I don't think either will run Bilgewater in the end, probably once they're completely exhausted by the fighting, Noxus is going to swoop in, impose order on Bilgewater, and have both of them executed.
But disregarding that grim prediction? Gangplank. At least there was some semblance of order when he was in charge. After Miss Fortune dethrones him, the town turns into the fucking Purge.
Gangplank is the most optimal choice.
I mean with him in charge Bilgewater basically rules the ocean. He can trash Noxus, screw with Ionia, its not hard to see how powerful and important Bilgewater becomes with a strong man at its helm.
But Miss Fortune? She doesn't even have any worldy ambition. She just wants vengeance. She would not be a prime candidate to lead Bilgewater.