Really interesting question. I would class myself as Polytheistic - I wouldn’t want my steel string acoustic or my Tele to have the same neck as my classicals, and I would find a classical with a Tele/steel string kind of neck to be utterly useless.
(At the Montréal Guitar Show this year, I got to play a classical made by Linda Manzer for Pat Metheny. It was a beautifully crafted instrument with neck that was about 1 5/8ths and, while I totally understand its appeal to a jazz/rock player, I hated that axe.)
I care far more about the width of the neck than the profile. I don’t like to go any narrower than 1 3/4s, and even at that, there are some classical pieces that just won’t transfer over to steel string or electric. 2 inches on all my classicals - that’s just a requirement. My 8-string has a 1 3/4 neck, and as a result it isn’t as useful a guitar as the Tele - there’s just not enough room to spread the strings apart like I’d like. It’s my most collectible guitar and my least useful. There. I said it out loud. You still can’t have it, though…
It has been really interesting switching between a 64 cm and 65 cm scale length, too. It doesn’t take me much time at all to switch between electric, steelie and small-scale classical. Switching between the two classicals has been really odd, though I’m getting used to it. I didn’t go for a fan-fret on the Baritone, partly because I’ll be switching between the two guitars in the same concert, sometimes in the same set, and I just don’t know if I could get my fingers around the fan-fret/straight fret difference in time.
I prefer a D-profile on the neck, but I’ve played slim line necks as well and not hated them. The one thing I just don’t like is a V-profile - I was looking after a friend’s Martin for a year while he was in Japan, and the neck profile on that just forced me into a thumb-wrap, whether I liked the idea or not. (I almost never thumb wrap, mostly because my thumb’s too short. I’ll occasionally slip the low F# into a D chord, but that Bruce Cockburn thing where he thumbs the low G in a C chord is just beyond me.)
I find Breau-barres (Breau barres are my nickname for when you play two adjacent strings at the same fret with the tip of any finger while leaving the strings on either side free to be played open, or with a lower fingered note. Can be done with 1, 2, 3 or 4.) difficult on the classical, much easier on the steelie, Tele or 8-string, but ‘5 o’clock bells’ sounds so much better on the classical so I live with it.
For me, the acid test on a classical is the Villa-Lobos 4th Prelude. Third phrase of the opening, the melody goes F#-E-D-C on the fifth, B-G hammer to the A on the sixth and hold it for a whole bar while the chord which follows goes A F natural, C, B, E using the open fifth string for the repeated chords. (1) - 0, (2) - 0, (3) - 5 with the fourth finger, (4) - 3 with the first finger, (5) - 0, (6) - 5 with the third finger.
He wanted to hear the A of the melody sustained all the way through the bar and the chords diminishing so that the melody A could be heard over the chords. If the strings are too close together, you’re either going to clam the open A with 3 or with 1, or you’ll accidentally bump the sixth string with the right hand thumb and cut off the melody A. (2:23 in this link for how beautifully Julian Bream does it.) If I can’t play that passage without clams, I’m not going to like that guitar.
Long, rambling and incoherent, even for me.