I have 3 vintage strats (57, 60 & 63), and 3 vintage teles (58,59 (slab board) & 62). This gives me a maple, slab board and veneer board for the Strats and Teles. I also have an MIJ 62 tele. In terms of neck shape, the MIJ matches the real 62, however the 'feel' is really different. All of them are different to each other, but they are all very different to newer ones. The only new 'relics' that have the same feel are my Bravewoods (though my 56 Bravewood used the 57 V-neck as a template. I haven't owned a CS, but I've picked them up in the music stores. I know you really need to have it in the house to tell but in terms of the feel, they were closer than the MIJ.
The old maple necks have a different feel to the newer ones, though the one I would like to try is the Eric Johnson. My 63 strat has a much fatter neck than my 60, which gives it a bit more sustain, though I love the feel of the 60 neck. Pickup wise, the 62 tele is the only one that doesn't have BK's (when I got the Tele's they were good buys because they had SD's on them). The original 62 set is so close to the Yardbird BK set, that I would say this is what Tim had in mind when he set them up. My 58 has a set of original Black Guard flattops on it.
The Strats have different pickups, the 57 has Apaches, the 60 & 63 have originals (though one of the 60's was rewound by Tim). There seems to be more 'ring' in the older guitars when you compare them to newer ones, though the pickups can help there.
I've also got some other old guitars, 53-58 converison LP, 54 LP, 59 LP Jnr, 60 LP Special, 63 Firebird III, 63 Thunderbird IV, 65 Fender Electric XII, 65 SG Jnr, 66 Precision Bass, 67 ES-335, 72 John Birch J1, 73 Rickenbacker 4001, 74 LP 55 Special and some 60's Silvertones. The biggest difference that I see with them is the woods. They are typically much lighter than the newer ones (except my Electric XII, which weighs a ton!). This could be why they seem to be a bit more resonant.
I have to say that a lot of the newer guitars are getting closer to the feel of the older ones, and they are a lot easier to take out!