I've been a member of both and just switched back from Nuffield to Hartham.
Opening hours at Hartham are much better unless you want to go Saturday or Sunday evenings. They extended them recently. See the times below. Hartham open earlier and hence is the only one of the two I can go to before work.
Nuffield have a sauna and steam room and the pool is better. They also have high prices and play on the fact that, quote, they are a "private members club". This means you get a towel when you go in, only they issued an email recently saying they'd run out.
Showers and changing are smaller at Hartham but, hang on, it's a gym. You're sweaty and just need a shower and I've never encountered more than two others in there.
Hartham have just revamped their equipment. They have classes just as Nuffield do.
My advice is to go down and speak to both. Say you are choosing between the two. Approach one gym at a time and ask for a week pass to see if the facilities are right for you. Then the next week go to the other gym and do the same.
Nuffield opening times are:
Monday 06:30 - 22:00
Tuesday 06:30 - 22:00
Wednesday 06:30 - 22:00
Thursday 06:30 - 22:00
Friday 06:30 - 22:00
Saturday 08:00 - 20:00
Sunday 08:00 - 20:00
Hartham opening times:
Monday – Thursday: 06:00 – 22:00
Friday: 06:00 – 21:00
Saturday: 07:00 – 17:00
Sunday: 07:00 – 17:00