I haven't run Linux on my MB's, so I can't say how same-same hardware performance would compare between the two. I always have a Linux machine around, though, and have for the last 20+ years (Slackware on floppies!) -- and it always runs faster than Windows. Much of that probably has to do with the fact that it's simply running a lot less code, and that a lot of what I would do with an app you do from the shell in Linux.

Regarding the narrow question of memory usage, I'd be surprised if Linux uses as much memory as MacOS, again because of the more extensive set of system services that runs in MacOS.