So, the results of a practical test I just did. Note that the incoming missiles were from an NPR, and were 30,000 km/s size 9 missiles with 2 decoys each (I think). Also the incoming missiles were magneto-plasma to my ion engines, so my AMMs barely had a speed advantage. I only counted the number of missiles hit, I ignored decoy hits. My ships moved away from the incoming missiles at 6,250 km/s.
Missile fire control: 2.89 million km range vs size 10 missiles, fire 3 AMMs per incoming enemy missile.
Multiple Warhead AMM: 55 enemy missiles destroyed, 640 AMMs expended.
Retargeting AMMs: 172 enemy missiles destroyed, 640 AMMs expended.
AMM Designs:
Multi-Warhead AMM
Missile Size: 2.000 MSP (5.0000 Tons) Warhead: 1.500 (MW-3) Radiation Damage: 1.500
Speed: 34,200 km/s Fuel: 137 Flight Time: 106.6 seconds Range: 3,645,720 km
Cost Per Missile: 2.285 Development Cost: 239
Chance to Hit: 1k km/s 342% 3k km/s 114% 5k km/s 68.4% 10k km/s 34.2%
Retargeting AMM
Missile Size: 2.000 MSP (5.0000 Tons) Warhead: 0.500 Radiation Damage: 0.500
Speed: 33,000 km/s Fuel: 137 Flight Time: 108.4 seconds Range: 3,577,200 km
Retarget Capable
Cost Per Missile: 2.275 Development Cost: 238
Chance to Hit: 1k km/s 330% 3k km/s 110% 5k km/s 66% 10k km/s 33%
I didn't even bother with trying ECCM or terminal guidance, because neither provide nearly as much as an advantage to an AMM as retargeting or multiple warhead.
Ultimately, Retargeting is clearly the best option, because it gives the AMM way more tries.
The AMMs are first fired at a distance of 2.8 million km. It take about 45 seconds for the AMMs to intercept at a range of about 1.8 million km. It then takes the enemy missiles 70 seconds to travel to 80k km from my ships, which was where I ended the tests. Thus, each AMM has a maximum of 14 tries to intercept a missile (first AMMs travel 1.485 million km to first intercept, and wont run out of fuel before the enemy missiles hit), although the number of possible attempts decreases as the missiles get closer.
In comparison, the Multi-target AMM effectively only gets 3 attempts per missile, 1 for each warhead. Every warhead I add needs 0.225 MSP of space in the missile (0.125 of warhead, 0.1 of multi-target bus), so I can only have a total of 3 warheads before the multi-target uses up more space than the retargeting module does. Yes, I could use smaller warheads against size 9 missiles, but a difference of .0125 per warhead basically doesn't matter, and going any smaller means introducing a risk of not destroying the missile when you do hit.
In conclusion, the only case you wouldn't use retargeting AMMs is if it is absolutely impossible to match the speed of the enemy missiles.