Your test game so far shows just how high fighter losses can be when engaging even with an advantage. And so far they've been lucky enough not to run into an AI AMM ship, which can absolutely devastate beam fighters. It'll be interesting how well they handle the logistics of an extended campaign.
I keep seeing people say this and I find it hard to believe, unless people are using their fighters in a suboptimal manner.
Considering typical ion-age technology, NPR AMMs at ion tech fly at perhaps 56,000 km/s (using a missile calculator; currently I think it is closer to 48,000, but I expect this to go up now that NPRs can research fuel efficiency techs). Beam fighter designs vary a lot, but a typical 500-ton, 4-shot 10cm railgun fighter can easily achieve 10,000 km/s or greater speed. Let's slightly underestimate this and say our fighters fly at 1/6 AMM speed, knowing that we can improve on this pretty easily. Then a 500-ton railgun fighter will on average shoot down 2/3 of a missile in final fire mode, or every 750 tons of railgun fighters can account for one missile on average.
Typical NPR AMM cruiser designs tend to be in the range of ~20 AMMs per volley and ~15,000 tons displacement, which is about matched by the same tonnage of railgun fighters - and again, we can do better than this without too much difficulty.
The question of course is whether this works out in a fleet context. Nominally, every ton of beam fighters must be matched by about another ton of carrier, as a practical rule of thumb (I think this is true in Steve's BSG campaign for instance), so in theory a fleet of pure AMM ships will outmatch a fleet of beam fighters plus their attendant carriers at equal net tonnages. In practice, there are a couple of caveats here, for one no NPR fleet is composed solely of AMM ships as this would be silly, for another the carrier fleet can take advantage of significant BP efficiencies such as using low-boost engines - plus, since components like hangar bays remain constant in build cost they become relatively more efficient as tech level advances.
As far as missile vs beam fighters in the general case, I think it is hard to draw a line between tactical and strategic effectiveness. If you use missile fighters, you have to replace the missiles fired and ship them to the front, but if you use beam fighters you will likely have to replace lost fighters and ship those to the front. Fighters do cost more than missiles, but you will only lose some fighters whereas you lose every missile you fire whether or not it kills anything. I'm not sure which is likely to be cheaper, but I suspect it will depend on the opponent and how effectively they can defend against both types of fighters. It also matters a lot if you are fighting NPRs or other player races, as in the latter case every tactic has a counter-tactic whereas the NPRs are usually predictable and exploitable.
But perhaps the meson needs to be revisited (just in general, not just for fighters) and make it not so underwhelming.
I actually played around with this a bit in my modded DB, and you can make mesons decently more effective just by improving the rate at which the armor attenuation tech improves. I'm not currently using that change as frankly the calculated efficiency of the mesons frightened me off, but I think I will try it in a 2.0 campaign to see what it is like in practice.
Everyone seemed focused on a purely offensive comparison between beam and missile fighters. A fast fighter with a high tracking speed and fast-firing guns is ideal for point defence. Missile fighters have no defensive capability.
Because this function is strictly inferior to turret of same size...
This is untrue. Turreted Gauss does become strictly the best beam PD at high tech levels (ROF 6, 8) but this requires a substantial research investment over the good ol' 10cm railgun method, which on large ships is about equally effective when compared to Gauss ROF 4 and is often "good enough" compared against higher-ROF Gauss cannons if you want to save on research costs for a long period of campaign time.
Compared to ship-based railguns, fighters can achieve similar or even greater efficiency because they can fly as fast as a turret can track. A 6-HS Gauss single turret with 4x racial tracking speed is nominally 440 tons and still needs a fire control, so is about comparable to a 500-ton railgun fighter with 3x EP modifier which can reach 3.5x to 4x racial tracking by engine boosting alone. The railgun fighters of course have the added strategic advantages that come with being fighters including - if needed - superior offensive capabilities to Gauss turrets.
As Steve has been saying, the strategic flexibility of beam fighters while still performing decently in multiple roles is the big advantage they have over any other more-specialized weapons.