I don't think that you can reasonably compare the to in regard to resources as they are too different in the levels of protection, shields, etc. But, many have found avast to be lighter in regular use than MSE (less of a performance hit, could indirectly be resources).
Whilst the AV Comparatives gives a good overall idea and considers both avast and MSE to be equal, this doesn't always seem to reflect real life and some of the experiences recounted in these forums.