Nostalgia aside, for those using it for target and hunting—accuracy.
The space between the cylinder face and barrel is less than a swing-out cylinder. Since the cylinder is fixed on both ends, it is supposed to line up to the bore better. Some would argue reliability, but most quality revolvers already have pretty high marks there.
I suppose it would be like comparing a semi-auto to a bolt-action rifle—less moving parts help with consistency/accuracy.
For me personally, the previous answer is completely hypothetical since I haven't attained the level of marksmanship where I can blame my firearms for any lack of accuracy. If I am not shooting well, it's usually operator error.