I will start right off the bat by saying that I do believe there are a few balance issues, but not quite as severe as the OP posited.
One of the biggest factors that I feel affects in-game 'balance' is the random mission draw, and not just one but TWO (you+your opponent).
THIS IS NOT A BAD THING, this adds extra depth to the game - two players sometimes working toward wildly different purposes makes for some cool dynamics.
HOWEVER!, If you only have one master&crew, you are, in general, at a gross disadvantage to those who have the options of their entire faction.
I play Neverborn the most, so I'll use them as an example.
Pandora - I HATE Treasure Hunt and Reconnoiter with Pandy. I don't like it when my opponent has those either. She just isn't mobile enough with her primary crew choices to really make these fly.
Lilith. She's our go-to for tricky situations. She's not the best against crazy ranged attacks (guild), but if I've got you in melee then I've eliminated your shooting (and probably already won).
Her crew can be crazy-fast with the right cards, making assassination, treasure-hunt or Recon a dawdle.
The only time I'd think twice is against Viki. The Ronin are just too fast and hit too hard... Pandora might be better in this case, depending on the scenario.
Zoraida. She's not as offensive as Lilith, or as Passive-Aggressive as Pandy, but for certain situations she's aces. With the voodoo doll and obey she can be insanely frustrating to play against. Nothing is funnier than making a Ronin stab Viki over and over and over (or anybody else you need to get rid of).
Her Silurid can be extremely fast and slippery to hit, making Recon and T/H pretty easy. They don't pack the wallop of the Nephilim though.
Nearly every master in this game has bad matchups or scenarios that are just a pain. Some just have a bigger list than others of things that are difficult for them.