How could that be? If you maintain a parallel bar then you will only be able to lift as much as your weak side. As long as we are talking about more simple movements like barbell curls, tricep extensions, esp..

It really just depends if your talking about a simple lateral descrepency in limb muscle strength or whether you are talking about more complex lateral (or other imbalances). From what this sounds like, bb should be the way to go, imo.