My Synapse install is using 94MiB of RAM and 500MiB of database disk space. CPU usage is effectively zero. I only have a 3 active users but decades of conversation history for myself (imported from other services). An uncompressed pg_dump of the data is about 250MiB which is within an order of magnitude of the raw text that I have in it. Nearly all of the conversations are encrypted so it wouldn't compress much.

Given that just running python takes 13MB of RAM it probably isn't using many resources past loading the code. At least at small scale running a Matrix server is not a notable resource burden for most people. A Matrix server written in a more efficient language (like Conduit) would likely be fairly similar to an XMPP server written in the same language. Either way unless you are hosting thousands of users it doesn't seem like this is a major problem for either protocol.