In talking about the Doom Shuttle build, especially vs. a HSF squad, I always thought Darth Vader would deal a crit but one of the guys said he'd have to go through the shields first.

They argue that since the enemy ship suffers 1 critical damage, it's like I suffered 2 damage (which may take out my shields if I still have them) to roll one critical hit on an attack dice, which obviously goes into shields first before it gets to hull.

I thought that since the text said "cause that ship to suffer 1 critical damage," it was like giving that ship a face-up damage card, no matter the current shield or hull values of that ship.

Which is which?

I really need to just make a blog post covering this in depth, for as often as it comes up

Dice results -> Damage -> Cards.

An effect can do any of the three - add results (like running over an asteroid), apply damage (like Vader), or deal cards (Proton Bomb). Any effect that does any of these enters the flow at that point, and then resolves.

When resolving damage (page 16) you remove a shield token if possible. If the ship has no shields, you then deal a card based on the type of damage - face down for normal, face up for critical.

Any damage, from any source, critical or normal, checks for a shield token first. That includes Vader.

I see. Hmm, that makes the job of taking down a HSF even harder. At least with the Squints and Phantoms that I like to fly with.

If an effect says to deal a card -- do that. Deal a card. See "Suffer Damage vs Deal a Damage Card" on page 8 of the current FAQ.

If it an effect says to "suffer" damage, follow the rules for "Suffering Damage" as described on page 16 of the rule book (which is, basically, that you get to remove shield tokens before dealing damage cards to your shieldless hull).