We've done both. Am 37 + 3, so ask me in six weeks' time for a concrete answer! Based on our experience, I'd say the main differences are the level of detail and group size.
In our area, you get a 3-hr NHS class on labour and birth, then a 2-hr breastfeeding session, both during the working day. Neither was really conducive to getting to know people, but the factual content was good, and the staff obviously know the situation at the local hospital, which was helpful.
The NCT classes we did covered the same subjects in 16 hrs, so were much more detailed and interactive, with six couples, and time to get to know each other.
We hesitated before signing up for NCT due to the cost, but were pleasantly surprised-it's made us both feel more confident about labour and birth, and our tutor was very objective. I was keen to do them partly so I would know what DP knew (if you see what I mean), and he found them useful - I feel much happier that he knows what he can do to support me.