One thing to consider is that it's incredibly easy to supply enough power for missiles; concussion missiles require only ~7 output per missile, while assault missiles require only ~4 output per missile. For comparison, epsilon torpedoes require ~10 output per torpedo, velocity shards require ~13 output per torpedo, shockwave torpedoes require ~16 output per torpedo, plasma thunderbolts require 20 output per torpedo when first developed and 32 output per torpedo once you research the first upgrade, and shaktur firestorms require ~18 output per torpedo at first and ~23 output per torpedo with the first upgrade. This means that missiles are fairly easy to fit in as a secondary weapon for a ship whose primary armament is energy-intensive.
Regardless, end-game missiles are an incredibly bad choice for a primary weapon when compared to end-game torpedoes (though the first two assault missiles do have a very minor range advantage over the first two plasma thunderbolts, at 740 vs 690 range for assault 1s vs plasma 1s and 880 vs 830 range for assault 2s vs plasma 2s) as missiles provide very low DPS per unit size. Comparing the Plasma Thunderbolt III to the Assault Missile III and incorporating the effect of the power requirements by doing the math for the total number of each weapon supportable by a HyperFusion Reactor II, you can find that the Assault Missile III will only equal the DPS per unit size of the Plasma Thunderbolt setup at 900 range, despite a HyperFusion Reactor II being theoretically capable of supporting 50 Assault Missile IIIs but only 6 Plasma Thunderbolt IIIs by reactor output; the limit by reactor storage is 24 Assault Missile IIIs or 6 Plasma Thunderbolt IIIs. If you go for the weapon limitation by reactor storage, the missiles can match the alpha strike damage per unit size of the torpedoes at 500 range, while the limit by reactor output leaves the missile alpha strike worse until 900 range.
Weapon Output Limit Size Storage Limit Size
Assault Missile III 50.2 (50) 716 24.4 (24) 352
Plasma Thunderbolt III 6.72 (6) 88 6.88 (6) 88
The number in parenthesis is the number of weapons used to compute the size. HyperFusion Reactors are size 16 and one such reactor was included in the listed size; the limits give above are the number of weapons you can support off of one HyperFusion Reactor II. Assault (cont.) refers to the 50 missiles per reactor limit, while Assault (alpha) refers to the 24 missiles per reactor limit. Since plasma is 6 torpedoes per reactor either way, it works for either. Note that this is favoring the missiles somewhat, as the total size of the missile setups is such that you could not easily fit multiples of the setups given, while the plasma torpedo setup can be mounted on a ship multiple times fairly easily.
DPS per unit size:
Range: 0000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000
Assault (cont.) 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47
Assault (alpha) 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45
Plasma 1.70 1.57 1.43 1.30 1.16 1.02 0.89 0.75 0.61 0.48 0.34
Alpha strike damage per unit size
Range: 0000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000
Assault (cont.) 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94
Assault (alpha) 1.91 1.91 1.91 1.91 1.91 1.91 1.91 1.91 1.91 1.91 1.91
Plasma 3.41 3.14 2.86 2.59 2.32 2.05 1.77 1.50 1.23 0.95 0.68
You can see from the tables above that Assault Missile IIIs work better when configured as an alpha strike weapon (reactor storage limit) than when configured as a continuous DPS weapon (reactor output limit), as the alpha strike per unit size more than doubles while the DPS per unit size is barely affected. Regardless, unless you're planning to only engage at extreme long range (i.e. 900+ range), you're better off with Plasma Thunderbolt IIIs than Assault Missile IIIs if you can't end the fight soon after the alpha strike. I'd also point out that the two assault missile configurations given are incredibly large, especially in comparison to the plasma thunderbolt configuration. While it should be possible to achieve these configurations if you have enough of the construction research, the missile configurations, especially the output limit configuration, leave you much less space to play with on the rest of your ship. Of course, the missile storage limit configuration is also only using about half the reactor output, so you at least don't need to worry too much about fitting additional reactors to cover cruise and static energy requirements on that one.
It should also be noted that the missile configurations can allow for a much larger operating range than the torpedo configurations, due to the much lower energy requirements which translate to lower fuel requirements. One reactor to power 700 size worth of Assault Missiles is about as fuel-efficient as you're going to get, even though it's not the most effective configuration in terms of DPS per size unit; ~700 size of Plasma Thunderbolts requires about 10 reactors, which means that you'd need about 10 times as much fuel for the same amount of combat time as the 700 size of Assault Missiles. Thus, the missiles are fairly good for use far from base or for extended deployments in low-fuel areas, for reducing the fleet's fuel costs if the fleet sees a lot of combat, and for generally increasing the fleet's potential time on station. Adding in fuel components to the DPS per size unit and alpha strike per size unit computations will also shift the balance towards the missiles as 1 fuel cell will provide the same amount of combat time for 700 size of Assault Missiles as for 72 size of Plasma Thunderbolts, so adding in the size cost of the fuel cells to provide whatever amount of combat time you want will more severely affect the torpedo DPS and alpha strike per unit size than the missile DPS and alpha strike per unit size.
You should also be aware that these tables are more valid for large warships than small warships. No small warship is going to have 700 size units dedicated to weapons; even the 336 size worth of weapons on the missiles by storage limit setup is pushing it in the end game. You can nevertheless see that the missiles aren't hurting that much in the DPS per unit size department despite paring down the number of launchers carried, so while the DPS per size and alpha strike per size figures aren't attainable for small ships they may at least be close, especially since a reactor supplying the power for missiles likely has more than enough spare power to cover a decent portion of the other power requirements for a small ship, and in this case the output limit and storage limit for missiles may become fairly close, meaning that you can choose a missile armament which makes full use of the excess output without going too far over the storage limit (which controls the number of weapons in the alpha strike).