As I said in my other reply, I think the difference is really ERoEI. And that's very likely an important difference. Because you wouldn't get an economical system if you're not able to get a competitive ERoEI from the whole system (including storage). I suspect to take oil's status you'd therefore have to have something that allows you to also cheaply get the energy, not only store it.

Lithium as an input to storage is really just a small part of the whole picture. Like a barrel is for oil.