In the case that there are two equal-difficulty-sum chains, the node processes whichever block it received first. They won't discard the second block, but they won't be trying to extend it if they saw the other one first. If MBC is behind Tor and the attacker studied the network latencies well, most miners will see the "legit" block first, and that "legit" chain will most definitely get extended first. (I'm using "legit" here, because I don't know any other way to refer to the non-attacker chain... there is, of course, nothing wrong with the attacker's block except that that chain is unlikely to get extended)
If transactions carry over between from invalidated chains, then the attacker should send himself a small transaction using one of the outputs he used in the huge deposit transaction, to be included in the "legit" block while he waits for it. By doing this, he guarantees that the large deposit is DOA on the new chain in case the nodes decide to carry it over. Otherwise, it's possible that the deposit will be transferred to the new chain and the double-spend fails.