And you know, I'm really glad that he met her. We always heard about what a wild man he was in his heyday.

She brings out the 'Hell bent for leather' ensign Picard. After all, the man was stabbed in the heart in a bar room brawl over what was basically a rigged pool game. Picard was the one who rigged it. Vash has him storming a castle single-handedly, all for the love of a maid.
But with Vash he could end up exploring some ruins or something after he leaves Starfleet instead of just making wine.

Exactly, The Vash character was a gold mine of untapped potential!
I don't want to get into a ship war, because ultimately it just comes down to what works for you as a viewer personally and there's no one right answer on that.

Agreed. That's why my co-author and I used to giggle at the 'Well, it's a good story, but how dare you pair Picard with Vash instead of Crusher' OTP reviews. We considered them badges of honor. If they took the time to read and review it then as writers we did something right.
I will say though that I firmly disagree with the idea that Picard's commitment to duty, honour, and obligation is a veneer. A 'cocky' Picard (who can handwave theft, vandalism, and the destruction of most of what archaeological science holds dear for profit from a longterm partner?) is not a Picard that I'd even recognise, tbh.
First we are talking about 'screen archaeologist' (Indiana Jones, River Song and such) not real modern day archaeologists.
However, that is exactly what canon shows us. According to canon, before meeting Picard on Risa Vash spent five years working as a personal assistant to Professor Samuel Estragon, an archaeologist who's work Picard knew. It was Professor Samuel Estragon who was originally hunting for the Tox Uthat. It was also Professor Samuel Estragon who hired the Ferengi Sovak to aid in his explorations, especially in situations that weren't quite ethical. Moreover, Picard isn't surprised at all and is amused by the idea. (3rd season episode Captain Holiday.)
PICARD: Any woman who can beat a Ferengi at his own game, bears watching.
Also in the 6th season episode "The Chase," Picard's own mentor Professor Galen comes aboard the Enterprise and attempts to BRIBE the captain with a Kurlan naiskos, very rare archaeological artifact, wanting Picard to leave his captaincy to become Galen's muscle.
GALEN
"... I'm sorry, Mister Picard. But that information has a price --your agreement to join me on the final leg of this expedition."
PICARD
"For how long?"
GALEN
"Three months. Perhaps a year. If we had a starship and complete diplomatic access -- a matter of weeks. But we'll have only my shuttle, the transports we can arrange, and our combined talents."
PICARD
"Why can't you do this without me?"
GALEN
"I'm not a young man. There will be hazards along the way. I don't want my own inadequacies to jeopardize the completion of this work."
In this episode Professor Galen is operating exactly the way we were told that Professor Samuel Estragon did and the way Vash did. Therefore, it is a believable extrapolation from series canon that fieldwork in interstellar archaeology can be a somewhat rough and tumble, wild wild west like business.
Warmest Wishes,
Whoa Nellie