A 50t EM passive sensor will detect a resolution 120 active sensor at roughly the same distance the active sensor will see you if they are built using the same sensitivity technology. A 100t EM passive sensor is equal with a resolution 20 active sensor in range. A 150t EM passive is equal with a resolution 5 active sensor and finally at 250t EM passive you can detect a resolution 1 active at the same distances.
If you look at the above numbers I would always install a 75-100t EM passive on all capital ships, it is a perfectly good life insurance policy. You then will have to figure how important it is to put bigger EM passives on smaller ships to detect enemy active before you yourself is detected. As you need a bigger sensor the smaller the platform they become increasingly more expensive to use on smaller platforms in terms of mission tonnage. Smaller platforms should likely be deploying more specialized ships and travel in larger groups, smaller platforms also are cheaper and so don't need the same redundancy that you want with larger more expensive platforms.
What you constitute as a large platform or small one are obviously hard to tell... but in general a ship at above 7-8k tons probably could afford a 75t EM passive sensor.
To add onto this:
The precise formula you can use to determine what mass of EM sensor you will need to detect another ship's active sensor before it can detect you is:
EM sensor mass in HS >= 16 / pi / Resolution^(1/3) * (active_sensitivity / passive_sensitivity)
Here, both sensitivities are EM sensitivities of the active (i.e. other ship's) sensor and your own passive EM sensor respectively. Resolution of course is in HS. I'll happily provide the derivation if anyone asks for it.
So for example, if we assume both races have the same EM sensitivity tech level, then using Jorgen's examples:
- If the other ship has a sensor resolution of 120 HS, the required sensor mass comes out to 1.03 HS; in game this would be rounded up to 1.1 HS which is 55 tons, a bit over the quoted value.
- If the other ship has a sensor resolution of 20 HS, the required sensor mass comes out to 1.88 HS; in game this would be rounded up to 1.9 HS (probably 2 HS as most players like to have a round number, or 100 tons as Jorgen says).
- If the other ship has a sensor resolution of 5 HS, the required sensor mass comes out to 2.98 HS; in game this would be rounded up to 3 HS (150 tons).
- Finally, if the other ship has a sensor resolution of only 1 HS, the required sensor mass comes out to simply 16 / pi or 5.09 HS; rounded up to 6 HS in game (300 tons).
As the highest EM sensitivity possible is 75, any product of EM sensor mass and sensitivity which is greater than 382 will always detect any possible active sensor outside of the latter's range at least by a slight margin. The first tech level at which this is possible is EM Sensitivity 8 at which point an EM sensor of size 48 (maximum possible size is 50 HS) will accomplish this. Of course, if you are going up against an opponent with EM Sensitivity 75 with such a low tech yourself, sensor range is probably the least of your problems...
More generally, since the EM Sensitivity tech increases by roughly ~1/3 at every tech level (the largest relative jump is 37.5% from 8 to 11, all others are 33% or smaller), an EM sensor of about size 8 will detect any active sensor up one tech level better outside of its range, and a sensor of size 11 or 12 will detect any active sensor up to two tech levels better outside of its own range. Beyond this size, bigger is still better for gathering information but the benefits are not as pronounced.
For thermal sensors there is not a clear-cut answer for what size is ideal, but they are certainly necessary to spot an enemy who has his actives turned off. Noting that the minimum thermal signature that can be detected is just 1 (conveniently, any ship at the 1,000 ton mark will have this thermal signature when idling its engines), the minimum range at which any thermal contact can be detected by a thermal sensor is (250,000 km) * SQRT(sensitivity * size). It might make sense for example to choose a minimum range that exceeds your active sensor range, so that you can use thermal sensors to sneak up on a target and then turn actives on to shoot them