A comparison will always be difficult because people that go to the USA have set aside 6 weeks or whatever, whereas people doing it in the UK are trying to slot it into their lives.
Sure the USA will be cheaper than the UK; the question is whether it's worth the extra trouble, and that has to be an individual decision. Some people will go to any hassle to save 10%. I would be suprised if it was more than 20%, by the time one has allowed for food (most American food is absolute trash and they are ahead of even the UK for obesity; for a 6wk stay you probably will have to go shopping and buy your own stuff; self catering).
The average PPL in the UK is probably about £8000 nowadays. This is based on the average time of about 60 hours. Younger people will do it in less (few, very few, do it in 45); older (50+) people often take 80 and I have met loads of 100+ hour students, mostly people in their 60s and over. I've met some £20,000 PPLs although I suspect a crooked school/instructor in those cases. Mine took 66 (early 40s and probably average natural flying ability) and cost £8500.
In the USA, this will definitely cost less, but then you can't mess around out there because your airline tickets and the Visa will expire
You have to get your head down and get on with it. It will
not be a holiday. One cannot take the risk of taking it easy and not completing; if that happens you will probably never come back. If I had failed my IR I would not have gone back and done it again (too hard and too much peripheral hassle).
A South African PPL is indeed an ICAO PPL but unless you just want a plain PPL it is a dead end. Once not doing a UK/JAA one, the FAA one is the only one worth doing because you can find FAA CFIs for the BFR relatively easily, etc. And the route to the IR is also well defined. Let's say one day you do the IR - are you going to be flying a SA-reg plane in the UK, to get the privileges of the IR? In flying, one needs to think ahead.
The real challenge if doing a rapid PPL, UK or USA, is to find a well organised school. It will have to be a bigger school with plenty of instructors and planes, so there is always a way to fly that day. My experience is obviously limited but I bet it's a lot easier to find such a school in the USA. The UK flight training business is for most part pretty dis-organised.
I would also go to Arizona or S California - guaranteed weather.