Upverter is working on a tool to help convert between all of those formats:
https://github.com/upverter/schematic-file-converter
Also their companies don't usually offer a choice. Big companies have a librarian who is in charge of the official part libraries. But if you could easily port an OrCAD library to Altium or Eagle or whatever, that would be a game changer, I think.
But we've got a newer version of this converter project that we are cleaning up right now. Its also able to do Altium, Cadence, and their libraries. Coming soon!