Here's Everyday Driver reviewing the C8 vs base 718 Cayman. Both guys scored both cars 4/4 but both picked the Cayman. One is a 981 Cayman GTS PDK owner, the other is/was an Elise owner who struggled to decide on the winner by a narrow margin and lost sleep over it. By indirect inference or proxy, that matches your intuition that the C8 would be a better comparison to the Emira. They have opposing strengths/weaknesses that strive toward supercar tendencies at the compromise of other things. Net, I think it would be a wash and depend on what you prefer. Whereas Cayman is the jack-of-all trades that compromises nothing and, thus, gives nothing up in exchange for supercar tendencies in any specific area.
Another proxy review is the Evora GT vs C8 (not the most tasteful reviewer but I at least respect his unfiltered honesty and hobbyist POV). Evora wins overall mainly due to visceral feel whereas the C8 beat it only in looks. Emira beats the C8 in looks by miles but then some visceral edges the Evora had are softening in the Emira. Question is by how much? I'd guess Emira is still more visceral than the C8, especially with its manual transmission.
Coincidentally my interest for the C8 ticked back up last week (but not in anticipation of this week's Emira reviews). I have a few 2023 build specs saved and budgeted. I'd be happy with either car as I appreciate each one's respective strengths albeit those strengths are different. C8 is looking like the more definitive bargain vs the V6 FE. But I'm queued for a V6 BE and its option pricing should help me decide. My dad is getting a V6 FE so it'll help me to test drive that but also tips me toward C8 for access to both cars instead of being crowded by two Emiras.