I don't think MSE uses more resources than Avast. Avast was always on equal footing with MSE here for years in the recommendations I saw given. But over a year ago Avast bloated up with a gadget and web app that was made hard to avoid for most users. That and the regisration nags trying to trick users into upgrading to paid version with dire messages turned many off to it, I believe. Meanwhile MSE became even more seamless and nearly disappears by comparison.
If you had problems with MSE or any app running up your CPU then I'd reinstall it. I see occasional repeat errors in Admin log for MSE which I simply google and then resolve nearly effortlessly. Other than that I see no problems with it on countless thousands of installs.
That said, use what you're comfortable with since you must be inured to Avast scare messages now.