You can mine Filecoin by providing storage for their global distributed network. I find this a wonderful idea, an elegant solution to a complex need.
Whereas bitcoin (which is legendary) is a value container, this filecoin is a blockchain with a very specific utility. Humanity will always have a need for storage. So they occupy a space that guarantees them some market share in the future, forever. Sure, maybe it will be ultra-competitive, or something else happens and somehow there will be free infinite storage forever, but at least in the present, filecoin seems like a wonderful idea. Especially if it’s done right.