So what kind of numeric advantage does a fleet need at TL-15 that is NOT equipped with meson tech to defeat a TL-15 fleet that does?
First pass analysis: a LOT!
Every time a f-J or better meson gun fires, it has about a 10 to 20 % change of mission-killing a target, even through f-9 screens and config-1. Every hit kills a lot of missile batteries. To have a good chance of getting one kill per squadron salvo we need 4 to 5 BRs, so that's 100000 to 125000 dtons of rider to kill one enemy ship per turn.
To return the favor, the missile/PA-armed ships need to get enough Wpn-1 hits (against f-15 armor and f-9 nuclear dampers) to reduce the spinal mount below f-E or so (any smaller and there's a good chance that the meson gun won't roll the instant death "Fuel Tanks Shattered" hit). So we need 35 hits (5 on the MG, and 5 for each of the other weapons: laser, energy, missile, PA, repulsor, sand). A single f-9 missile salvo has a 10% chance of penetrating the defenses,and gets to roll one on the Surface Explosions table and once on the Radiation table. One-third of the Surface Explosion hits will be Wpn-1 hits against f-15 armor, and just over 40% of the Radiation hits will be Wpn-1 hits, so we need around 45 hits to get our 35 Wpn-1 hits, and we need 450 missile batteries to get our 45 hits, so we need 450,000 dtons of missile-armed ship to mission-kill 1/5th of our 125,000 dtons of BR in one salvo.
Looks just about 5 to 1. Spinal PAs would make that better as they would get more damage rolls in less tonnage, but not much more, as the f-15 armor would reduce even a f-T spinal PA from rolling 19 times to only 4 times (on both the Surface Explosion and Radiation tables, so it's actually 8 rolls total), which is only 2 more damage rolls than you could get from replacing the 3000 dton spinal PA with 3 extra missile batteries.
Here's a real difference (in my eyes): those ships "killed" by the meson guns are either really dead, or so crippled they can't escape. If their side doesn't win, they are prizes to the enemy (from lack of power, lack of fuel, or lack of crew). The ships "killed" by the missiles are just firepower-killed, they still have drives, crew, and fuel and can easily escape by acceleration or by jump.
Anyone want to check my figures?