It sounds like you like the S2000 'feel' better for overall fun - the FR-S/BRZ is pretty close to that car in 'spirit', especially with a few 'must' mods like a good header,tune, and better tires. More visceral, more focused, less refined.
Cayman is a more refined package - more like a comfy BMW than an S2000 (but still with outstanding driving dynamics).
The two are completely different animals - the thing with the FR-S/BRZ, is you really need to drive one with those 'base' mods I mentioned - changes the car pretty significantly for the better IMHO. Cost for the tune & a good header mods will be between $1000 and $2000 based on what you get, which is not too bad (and worth it in my opinion).
Lastly I'd like to re-point out what someone else posted in this thread - practicality. The FR-S/BRZ kills the S2000 & Cayman for practicality. It's such a well thought out car in that regard - the back seats are tight, but I carry my whole family (me, 6'2", wife 5'10", kids 10 and 12 and fairly tall) around in the back seat all the time for trips < 1/2 hour. No leg room but they sit cross legged - the back seats are deep and tilted back allowing them to be relatively comfy for short-moderate distances. Or I can lay the rear seats down and have a ton of trunk space, I've carried 4 18" rims with tires in mine. Try any of that in a Cayman or S2000
Also most cars with a useable 2+2 layout end up looking 'stretched' in the rear, proportions get skewed. The FR-S/BRZ has beautiful proportions.