Bridge Packs - As far as I know, any bridge packs purchased through the C-Store can be used for any ship, regardless of the ship's type. For example, I purchased the Prometheus Pack, and I've used them on my science vessels. I even have them as options for my Lieutenant Engineer that is currently flying the NX-Class.
So, like I said, I think the bridge packs purchased through the C-Store are usable on any ship. (I can't speak for the Defiant ones, because I didn't purchase them. However, all the packs I did purchase are usable on all my characters' ships and ranks.)
Borg Bridge Officer - It's not the same one that you get from the STF, but it is the same one that was included with the Amazon pre-order. She's an Engineer, while the STF one is Science. Her appearance is adjustable as well, while I've heard the STF one isn't.
Also, they changed the Efficient trait a little while back so that they don't stack. If your Captain has the Efficient trait, it will stack with one of your officers, but two officers won't stack.
Hope that helps.

(And, if I've gotten anything wrong, sorry. I'm sure I'll be corrected by someone, if I have, lol.)