My first idea would be to let the Spocks discuss it, it IS their life, after all. Being rational, and willing to make personal sacrifice, I think they could come to some satisfying conclusion. What Lord Raziere said sounds like something they would come up with.

However, if for some reason I had to make a decision, I'd take the meat-brain Spock, for the same reasons others have given, namely that the brain is the seat of the mind, and that brain is the older of the two Spock-brains.

As for the ship of Theseus problem: the ship of Theseus is whatever ship Theseus happens to have sailed on, it's not neccessarily bound to individual physical components. Such, each new part Theseus replaces becomes part of his ship, while each old part he throws away does not stop to be part of Theseus' ship. Just not a part of the ship as it currently is.