The Fediverse - especially the microblogging side of it - has deep issues when it comes to environmental sustainability.
And the high resource requirements, which result from an incredible level of redundancy, aren't just bad environmentally: they make running a server more costly, and increase our reliance on Big Tech's infrastructure.
I wrote about all this, along with some suggestions for how we can improve things somewhat.
That's a good question. The best answer is, I don't know!
But if I had to guess, based on the small amount I've learned:
larger servers most likely benefit from economies of scale. They'll be using CDNs, and will often have several people on their server following any given remote account, rather than just one. So the per-client energy use is almost certainly lower than for small servers.
But it's still tough to know whether it's the client or server using more energy. IIRC with video streaming, the end user's device was a big factor in overall consumption - but it's not like the server is chugging away 24/7 fetching media for you like a Fediverse server is.
For single-user servers, or servers with only a few accounts, I expect the server (and all the network infrastructure in between two servers) is doing a lot more work than the client(s) - unless it's like, the server is on a raspberry Pi and the client is running on a powerful desktop for a lot of the day, or something. Again, many factors at play.
Really though, the question I start to ask in all this is more about, which parts of the system are the most difficult to justify?___