The resolution is the target HS that it's made to detect. Anything outside that optimal size gets a range penalty. Your 1 resolution may track targets at 50,000 km, while your 100 resolution may track targets at 5,000,000 km. But your res1 is going to track 100HS at even less than 50k, and your res100 is going to track 1HS very poorly (not at all, honestly) and detect 500HS at shorter range.
Understanding your enemy is key. If they're sending fighters at you, then your battleship sensors are worthless. If you're fighting a 60,000 ton swarm queen, then your fighter sensors are pathetic, and your battleship sensors are probably worthless. But a 1,200 resolution sensor may see that queen at 5trillion km, because larger targets are easier to spot.
Crusty: Most people develop a lead fighter. 3 Hangar Decks packing 5 beam fighters and 1 where it's mounted a sensor instead of a beam, same as you'd expect in large ships. In this case, it's the same as large ships, yeah. You can fit them all with a sensor and have redundancy, or shave space and fit it on just one. I personally design my fighters for close-in support, striking at some 50m km and harassing the enemy before the battleships arrive, but if your fighters are heading out beyond your sensor range for deep space ops or long-reach, then you'll want sensors on at least a few fighters.
EDIT: I usually like to make a 20HS FAC with the sensor, try and match the speed with the FAC engine (usually not possible) and mount some heavier armor and maybe a CIWS on the FAC. Give yourself a tiny sensor corvette, they usually work well in main battleship combat as well, simply to have an extra pair of eyes available.