I visited the USS Constitution right after an extensive restoration in the '90s. I asked one of the officers just how much of the original ship was still here and he said very little. However, he also said she was still the Constitution and where can you see another one like her.
The detaily stuff about the TMP refit is interesting. Like how the transporter room is located in the same place in an axis corridor just off a circular corridor that it was in TOS. Also, when Kirk and Decker are conversing in a corridor intersection, you'll notice over Kirk's shoulder that you can make out the rectangular shape of the old corridor at the intersection. Nice set design to make the new corridor set look like a retrofit.