So, a resolution 1 sensor is... good for anything? Why would you never use anything but resolution 1, then? Is it range penalty?
Its simple.
The range is multiplied by the resolution.
A resolution 1000 sensor would detect a size 1000+ ship at 1000x the maximum range of a resolution 1 sensor. There are penalties for smaller ships of course.
A resolution 100 sensor detects a size 100+ at 100x the range of a resolution 1 sensor.
A resolution 1 sensor has a 1000x or 100x shorter range but will detect anything in that range.
It is far more efficient to tune the sensor for exactly what you are trying to detect.
...could you put a whole shitload of sensors of varying resolutions on one ship?
First of all, it turns out the range is more complicated than just multiplied by the resolution. Not sure about the whole formula, but it's probably what was posted earlier.
There's no reason you can't, but you'd probably get better results from having a few, larger sensors.
For example, lets try to figure out all the types you might want. Size 1 for missiles, size 4 for fighters, Size 16 for FACs/Star Swarm, Size 45 for scout ships, size 120 for small warships, size 300 for full warships, Size 500 (max) for capital ships. That's 7 sensors.
Take Missiles and fighters. If instead of two sensors you made a Resolution 1 sensor that was twice the size, it could detect fighters at the same distance as a size 1 resolution 4 sensor, but would detect missiles at twice the distance. Similarly, if you combined the resolution 16 and 45 sensors into a size 2 resolution 16 sensor, you'd get one sensor that could detect both types at a longer range. After resolution 120 I'm not sure there'd be much benefit, as at that point they're extremely long range anyways.
The maximum I could see any ship reasonably having would be 3; one point defense/antifighter, one anti small ship, and one anti large ship. Small differences in size/resolution don't penalize range much, so trying to cover every possible size has diminishing returns.