Mass Accelerators: missed potential
It is already known that the main gun of a Mass Effect dreadnought accelerates its payload to roughly 4,000 km/s. As discovered via math (with a bit of help from the previous chapter) the council races have the ability to reduce mass (at least) to the degree that expending 1 m/s worth of delta v can accelerate a ship by 3,000 km/s. If the interior of a mass accelerator were even mass lightened by 1% of the intensity used in an FTL drive that means that the dreadnought's main gun is only applying enough energy to accelerate its slug by 133.333 m/s. To put this into context, the muzzle velocity of the colt m1911 is ~250 m/s, which would (if mass lightened to the same degree) accelerate its bullet to a terrifying 7,500 km/s and deliver 337.5 gigajoules of kinetic energy to its target (which is roughly equivalent to ~80 tons of TNT). The theoretical railguns the U.S. military are testing have an (expected) muzzle velocity of 5.8 km/s, which maps to 174,000 km/s (to put that in context, the speed of light is ~300,000 km/s). And advanced "FUTURE TECH" railguns would likely be even more powerful, thus getting into the 'FTL field collapse' scenario detailed in the previous chapter.
Worth noting is that the infantry scale weaponry is still reasonably accurate, as you would rather have higher ammo capacity than have individual soldiers toting WMD rifles. However, given that the bullets in mass effect guns are sheared off a single block of polymer it would make sense for there to still be a "whatever is in front of me will die in the next 3 milliseconds" mode. In addition, pre-eezo firearms modified with mass-lightening systems would probably become extremely popular black market items (though they would probably have settings ranging from 'normal rifle' to 'who needs nukes?' for varying purposes). It should also be noted that these hypervelocity shenanigans will be absolute hell in terms of barrel wear, and bullets fired in an atmosphere will tend to ablate into plasma, they also have the potential to trigger nuclear fusion as they travel.
It is worth noting, however, that mass accelerators have uses beyond destruction (as detailed below)
Energy: eternal power
As you may have noticed, mass accelerators "cheat". When the slug is being accelerated it uses far less energy than normal to reach an absolutely insane velocity, then once it leaves the mass effect field it suddenly gets an awful lot of kinetic energy from absolutely nowhere. The question in this case is "what would happen if I had a wimpy mass accelerator set up like the piston in an internal combustion engine and connected a whole lot of them to a drive shaft that was cranking a generator?" This is a very good question. The "piston", assuming it massed 1 ton and delivered 1 megajoule of energy per hit (and yes it does have to be a hit, for reasons detailed below) would only need to be moving 44.7 m/s, which is trivial for a mass accelerator. However, if it's connected directly to the crankshaft, that has its normal inertia, which necessitates that the piston either be separate from the slug (which acts as a hammer against the piston) or that the crankshaft be mass lightened (more trouble than its worth).
A "supercharged" version of this is something I personally prefer to call the particle beam turbine. In it a mass-lightened hall-effect thruster (for example) which would normally accelerate its throughput to ~60 km/s instead accelerates its payload to relativistic velocities (indeed, the particles are actually superluminal for a brief period) thus multiplying the input power by some insanely huge number I can't be bothered to calculate once they leave the area of high-intensity mass lightening. This stream of relativistic particles is then used to (as the name implies) spin a turbine which is used to generate electrical power. This also has the effect of inducing a significant quantity of net thrust in the direction of the turbine. This can still work when a ship is at FTL (albeit at reduced power) as long as the accelerator portion of the device has a significantly higher degree of mass-lightening than the turbine part. In any case the primary limits to the system are how much abuse the turbine end of the device can take from constant bombardment with relativistic xenon atoms (or other such things). To counteract the thrust when you don't want to go anywhere it's generally a good idea to have multiple particle beam turbines operating in opposite directions.