Rails require no more hardware then scope mount bases.
They both use scope rings clamped somehow to the rail or base.
Weaver scope rings for instance, will fit either Weaver bases, or Picatinny / STANAG rails.
It seems to me rails are best employed on target style rifles where it may be necessary to have built-in elevation in the rail to get enough scope elevation clicks for extremely long range shooting.
Or on military type TackyCool rifles where you want to also mount a bunch of accessories such as magnifiers, back-up iron sights, night vision equipment, etc on the same sighting plane.
Bases are much more suitable for sporting & hunting rifles, because they are lighter, smaller, and take up much less room over the loading port on a bolt-action.
There is no disadvantage as far as strength or rigidity, as either one is mounted to the receiver with the same scope-mount screws.
rc