I have also used both types without issue but I did read an article that the Weaver/weaver style bases are the strongest design. Not saying this is true but (and I can't rememeber where I read it) it does sound logical.

You never said what gun this is going on, but I have fallen in love with the one-piece mounts, like the DNZs. IMO, there is nothing more stable or easier to install.

http://www.dnzproducts.com/game-reaper-mounts