Also, lots of use of robots for repair.
One has to look at the rationale in each universe. So, Star Wars has big crews because it is the old Space Opera feel, because there are lots of tasks, and simply due to the ships being so big, and the availability in that universe of lots of crew personnel.
In Star Trek (TOS) there are a lot of science specialists on the Enterprise, and about 80 security men (about 20% of the crew of about 430).
One also must ask questions such as is gunnery control almost 100% automatic, or does it require a gunnery crew for each gun.
One has to look at each possible duty station on the ship and what crew it requires. Especially important is the nature of combat in your universe - does one need security men to repel boarders? do you need soldiers on ship to raid less advanced planets? etc. Are crewmen/positions very specialised? Ideally, every crewman will have some training in Damage Control. And don't forget the robots.
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A side question to consider with regard to damage repair is does your ship carry enough spares and supplies? This is why TNG is so stupid - have no spare warp core, for instance. And does it have the machines and workshops to do significant major damage repair (or are you using super-nanotech)?