You could make an argument for either for both servers and clients to be quite honest.
You can run a server on 512MB RAM when hosting for ~5 people, but when not backed up the the CPU horsepower (eg. on a raspberry pi) it'll lag and won't be playable - similarly you could have a powerful CPU hosting a server for >50 people, but when you don't have the RAM to keep the world loaded, it'll lag and stutter as before
The client is a bit of a different story. You don't actually need the "8GB to keep everything running smoothly" as some people would like to suggest (I'm talking about vanilla here - modded is a completely different discussion). In my experience when playing on servers (and probably single player as well although I haven't tested it lately), you are perfectly fine with the 1GB that's allocated as standard and increasing it without reason is only going to make the memory dumps bigger and the already slow garbage collection even slower resulting in FPS drops and stuttering all over the place.
Here's where my level of knowledge drops a bit. In 1.8 the mojang team did make the client multi-threaded to a point. The world loading/unloading, villager AI, and some other things (that's escaped my memory, sorry) can be multi-threaded, and so reduce the strain on the thread(s) that is(/are) doing the rendering. This is where the argument for having a "stronger CPU" falls down, because you can't really measure how strong the CPU is for MC since it doesn't utilise, let's say the 16 threads on a 5960X, and a 4790K would probably outperform it because of it's higher clock speed.
TL;DR it depends on the number players on the server, whether you're playing modded, what you're doing in the world etc. Minecraft is a weird program and FPS numbers don't really make sense
some most of the time