Ok, I did throw together a few missiles with thermal and active sensors.
My techs are:
Magneto Plasma Drive
Max. Engine Power Modifier x2
Warhead Strength per MSP 5
Active Grav Sensor Strength: 21
EM Sensor Sensitivity: 11
Thermal Sensor Sensitivity: 11
First an ASM-6. Both variants dedicate 0.6 MSP to sensors/reactor
Missile Size: 6 MSP (0.3 HS) Warhead: 5 Armour: 0 Manoeuvre Rating: 10
Speed: 31200 km/s Engine Endurance: 33 minutes Range: 62.3m km
Active Sensor Strength: 0.3706 Sensitivity Modifier: 110%
Resolution: 100 Maximum Range vs 5000 ton object (or larger): 400,000 km
Cost Per Missile: 4.1829
Chance to Hit: 1k km/s 312% 3k km/s 100% 5k km/s 62.4% 10k km/s 31.2%
Missile Size: 6 MSP (0.3 HS) Warhead: 5 Armour: 0 Manoeuvre Rating: 10
Speed: 31200 km/s Engine Endurance: 33 minutes Range: 62.3m km
Thermal Sensor Strength: 0.2414 Detect Sig Strength 1000: 241,400 km
Cost Per Missile: 3.9763
Chance to Hit: 1k km/s 312% 3k km/s 100% 5k km/s 62.4% 10k km/s 31.2%
A hostile ship of 5000+ tons would have to have a thermal sig of more than 1657, to be spottet at greater range from the thermal sensor ASM than the active sensor ASM.
Of course, the thermal gets better, the smaller the enemy ship gets, as the thermal sig (and thus the range it can be spotted) decreases linearly, while the range of the active is reduces by the square.
Now an anti-figher missile:
Missile Size: 3.999 MSP (0.19995 HS) Warhead: 4 Armour: 0 Manoeuvre Rating: 13
Speed: 40000 km/s Engine Endurance: 12 minutes Range: 29.2m km
Active Sensor Strength: 0.2468 Sensitivity Modifier: 110%
Resolution: 5 Maximum Range vs 250 ton object (or larger): 60,000 km
Cost Per Missile: 3.6504
Chance to Hit: 1k km/s 520% 3k km/s 169% 5k km/s 104% 10k km/s 52%
Missile Size: 4 MSP (0.2 HS) Warhead: 4 Armour: 0 Manoeuvre Rating: 13
Speed: 40000 km/s Engine Endurance: 12 minutes Range: 29.2m km
Thermal Sensor Strength: 0.1612 Detect Sig Strength 1000: 161,200 km
Cost Per Missile: 3.5135
Chance to Hit: 1k km/s 520% 3k km/s 169% 5k km/s 104% 10k km/s 52%
My current scout-fighter design moves at 13,800 km/s, but I could probably get a smaller figher-bomber to move at up to 15,000 km/s, so lets run with those numbers. At that speed, it moves 75,000 km per 5-sec tic, giving my active sensor missile a 80% chance, the fighter will be in range after a 5-second tic.
That fighter has a thermal sig of 96, which means, the thermal sensor AFM will pick it up at a range of 15,475 km, which translates to a 20.6% chance to be picked up after a 5-second tic.
Finally an AMM
Missile Size: 1 MSP (0.05 HS) Warhead: 1 Armour: 0 Manoeuvre Rating: 11
Speed: 38400 km/s Engine Endurance: 2 minutes Range: 4.4m km
Active Sensor Strength: 0.105 Sensitivity Modifier: 110%
Resolution: 1 Maximum Range vs 50 ton object (or larger): 10,000 km
Cost Per Missile: 0.9236
Chance to Hit: 1k km/s 422.4% 3k km/s 132% 5k km/s 84.5% 10k km/s 42.2%
Missile Size: 0.999 MSP (0.04995 HS) Warhead: 1 Armour: 0 Manoeuvre Rating: 11
Speed: 38400 km/s Engine Endurance: 2 minutes Range: 4.4m km
Thermal Sensor Strength: 0.0682 Detect Sig Strength 1000: 68,200 km
Cost Per Missile: 0.8643
Chance to Hit: 1k km/s 422.4% 3k km/s 132% 5k km/s 84.5% 10k km/s 42.2%
1) Putting the space the sensor takes into agility doubles the to-hit chance.
2) A size-6 ASM, moving at 32000 km/s I threw together has a thermal sig of 9.6 and will move 160,000 km per 5-second tic.
a) The active sensor AMM will pick up a size-6 or smaller missile at a range of 1089km, giving it a 0.68% chance to notice an enemy missile after a 5-second tic
b) The thermal sensor AMM will pick up that missile at a range of 654km, which gives it a chance of 0.41% to pick up a new ASM after a 5-second tic.
Conclusion:
No matter what I tried, the active sensor missile always performed better than the thermal sensor one. The only exception would be an ASM, that is used vs. a target, smaller than the sensor-resolution. Then the thermal is better.
Vs. missiles, sensors, at least at my tech level, are absolutely, totaly useless.