I've watched both Outlaw Star and Firefly, enjoyed them both. And the only thing they really have in common of any importance is Melfina and River both being found in square shaped cryo chambers where both are in the fetal position and being naked, it's large, it's a big thing, for that one instant when it happens, then it's over with, and I can't think of anything reasonably that similar happening again in both series.
Looking at just Melfina and River -
Melfina goes into a liquid filled tube to help navigate and interact with the ship.
Melfina is of sound mind.
Melfina is not a fighter, and is worthless in any fight - unless it's her controlling the space ship.
Melfina has no family.
Melfina does not try to harm any member of the crew of the ship, or anyone else.
Melfina is a part of the crew, and is an irreplaceable member of the crew.
Melfina has a warm heart and develops relationships with the rest of the crew.
To me, none of that sounds like River, River is bonkers, she keeps her distance from most of the crew, threatens and attacks Jayne, her brother is her only real connection, she is for the majority of the time useless to the crew and ship.
As for the rest of the series?
The Outlaw Star crew fights pirates, goes on a space race, has catgirls (also known as some sort of alien species), have guns that seem to shoot magic, ships that have combat arms (arms that come out of the ship wielding guns and knives), there's little droids that zip around throughout the ship on zip lines, samurai, The crew starts out small and slowly builds over the course of the series.
The only characters I can think of that are even remotely the same are Gene and Mal, but that's because they're both fairly plain - Captain of the ship, who values his crew, is one of the best on the ship in a gun fight, and who dreamed of one day owning their own ship. Gene sits at the controls of his ship, Mal usually doesn't - Mal was a soldier in the war for independence, Gene's not a soldier, never been in a war.
Unless I'm forgetting a few things (haven't seen Outlaw Star in a number of years) the basics where - Firefly crew is on a beat up ship, that at times barely runs, so they need to take odd jobs just to stay a float, there end goal just to keep a float (which sounds more like Cowboy Bebop, but even then, give it a rest.), and the Outlaw Star is this super ship, where the crew is fighting pirates and trying to find a mythical land.
