Zcash uses a different mining algorithm (Equihash) that is so-called ASIC resistant. Bitcoin uses the Hashcash SHA256 algorithm, which is a completely different world. The Antminer is no good for mining Zcash, and GPUs are no good for mining Bitcoin.
The hashrate differs for each algorithm, so the Antminer’s 13TH/s is only applicable for the bitcoin algorithm.
EDIT: Don’t know if an equihash miner would refuse to run on an Antminer at all or if it only will yield extremely bad performance.
Neither. An ASIC miner like an Antminer doesn’t “run” a software miner; it just takes inputs to the algorithm it implements, and returns valid outputs. By definition, an ASIC can’t completely change the algorithm it implements in hardware, at runtime. So it wouldn’t even be possible to configure Equihash mining software to use an Antminer.