Animal protein is considered to be better than plant protein for lean muscle mass. So it depends if the shake is say whey or soy.
replyhttps://pmc.ncbi.nlm.nih.gov/articles/PMC7926405/#sec5-nutri...
I would hardly draw that conclusion from this paper. It's a meta analysis of a handful of studies with fairly low sample sizes, and it wasn't immediately clear that there was any controlling factor wrt amount consumed. There are also a lot of statements pointing out there was no statistically significant difference for various metrics...
replyFrom what I've read, both are good sources of usable protein but animal protein is considered higher quality because it includes more essential micronutrients that are delivered more effectively through the digestion process. Basically it's what your body has evolved to process best. Protein drinks do give quick protein for recovery, etc.
replyI won't call it common sense, but humans with highly limited technology lived and reproduced to build sophisticated civilizations in almost every biome on the planet.
replyOur biology is immensely adaptable, so anyone declaring you absolutely need some finely decided very specific thing in order to be "be healthy" should be treated skeptically.
With regards to protein specifically: your body doesn't trade in proteins as inputs, it trades in amino acids which cracked off the protein chains you eat. Everything else is just trying to keep the crowd of gut bacteria from making you feel uncomfortable.