I think the only real benefit of a Gauss pistol is that it fits well in a supply chain with Gauss Rifles. Similar bullet, similar tech, easier maintenance and supply chain. In terms of "bang/buck", I imagine a typical powder cartridge is more efficient, and even more capable. Gauss is specifically limited by barrel length and available power, powder pistols are limited by materials and structural integrity. How much pressure can a bonded superdense barrel and action contain?
Gauss recoil would be softer, even for the same energy, than a powder cartridge because the impulse is applied over the length of the barrel, not all at once. I would imagine that a gauss rifle is a particularly soft shooter, or has as much felt recoil as it contemporaries, but with more net energy out the barrel. We have that today, the M1A 7.62 semi-automatic rifle is known for much softer felt recoil than a generic bolt action due to the affect of the absorbing spring and bolt used for cycling. They also tend to be heavier, which affect felt recoil as well.
If you even want to see the advantages of gyro stabilization, go to a fine optics dealer and try on a pair of stabilized binoculars.
They're amazing! I never looked into how they work (it's not a gyro), but I think the net effect as perceived by the operator is the same. I don't want to suggest that stabilize binocular tech would work for a rifle. I don't think it would, as it stabilizes the image as presented to the viewer, not necessarily stabilizing the actual binoculars themselves. A rifle would need to actually be stabilized.
Mechanically, I would think that gyro stabilization would make "aimed shots" more accurate, as there needs to be a moment in time for the stabilization to take hold. I think it would help mitigate the need for casual rests (against door frames, etc.) for distance shots. But I do not think it would be as good as, say, a bipod or long standing rest.
Stabilization would only affect recoil perhaps is being able to limit muzzle flip and keep the rifle on target more quickly for a follow up shot. But wouldn't particularly affect felt recoil to the shooter.