I'm not Brady, but I would say "it depends". It depends on what you are comparing. My scope is a Swarovski 1.5-6x42. The non-rail version lists 15.7 ounces for the scope. The railed version lists 16.2.
Assuming good steel rings _and_ a riser or base equivalent to a riser, I would guess that it comes out about a wash in practical terms.
On the other hand, comparing the railed scope with a riser against a non-railed scope with high rings, I'd say the rings are going to weigh less than the riser, simply because there is more mass to a riser.
If you can use low rings on a non-railed scope or the ring-mounts for the railed scope, I'd say again that weight is a wash in practical terms.