Not quite sure what you mean by "travel options", but having been to both, I'd say Houghton- Hancock had more going on hotel and restaurant wise than Chama.
As for the mine, it is really amazing... they have a cool mine tour that takes you in maybe 3/4 of a mile? It was a long way in. If memory serves, the mine was about 6500 feet deep at the end. The fact that the hoist house and all the equipment (closed at the end of WWII) survived until now is pretty amazing. Many of the other mine hoist houses were scrapped, but due to someone's optimism, "old Reliable" sat there for decades.