Coming from a naval point of view, Escorts are like the Fast Attack and Balistic Missle submarines of Star Trek - Small crew, very manueverable, high damage. But despite this smaller crew and much less space for storage and facilities, our deployments are just as long as a carrier with a 20 times larger crew.
And just because a ship is smaller doesn't mean it doesn't have the amenities, they are just wherever they can fit. Life on a submarine is probably very comparable to life on an escort. Crew's Mess doubles as the movie lounge, exercise equipment tucked away in corners of the engine room, things like this. I could see an escort using the holodeck to double as crews mess as well as wardroom.