I think the main issue is that anyone can build a GF, but who can produce packs at one using current cell technology for under $133 (extremely conservative estimate) per kWh pack cost ($190 - 30% for GF reduction).
I think the other gigafactories (BYD, Samsung SDI, and LG Chem) will likely get close to Tesla's costs. But they might be behind a couple years. It's not like Tesla's GF is using some magical new technology. They're using mostly Panasonic tech, which isn't too drastically different than Samsung or LG's. GF is mostly benefiting from economies of scale, which BYD/Samsung/LG can also accrue as they scale their productions. Sure, their gigafactories might not be as large as Tesla's, but still they'll get nice economies of scale. (Example: BYD is projecting 34GWh production by end of 2019.)