The E-D lounge models did have more than just profile - they didn't exactly feature the saucers proportionately sticking out of the wall (which would have been tough to walk around), but they had more detail around various nacelles, etc.:
And hey, I was wrong about the E-E lounge - it DID feature the same six Enterprises on both sides of the main viewer:
Interestingly enough, John Eaves had made models of the shuttle, CVN-65, plus a non-refit Excelsior, Miranda, Intrepid, and Oberth (!) models to go in the "other" case opposite; however when he brought them to the studio he found they'd already put duplicates of the six Enterprises in both cases. It's silly to have a mirrored display like that, but I think I like that idea better than having to explain why four unrelated ship classes are in there too, or why the NX-01 isn't in there despite the show being on the air at that time (and stranger still that Eaves designed the thing).