Part III was er.... an experience. They say that even old Professors that have done the Part III speak of it like old war stories amongst themselves. I highly reccommend it because of the amount of mathematics and theory you can cover in a year even if you don't get the PhD offer from DAMTP.
I an international student from Asia but I did my undergrad at Imperial College London (The UK's MIT equivalent - Abbus Salam was our a head at one time) so I was pretty much acquinted with the English weather and the English by the time I enrolled at Cambridge. Anyway, the make up the Part III's are fairly international anyway. Lots of left-handed Germans, rigourous French mathematicians and very hard-working Chinese. There aren't that many Americans or at least I didn't bump into a great many of them so you'd be a minority which is a good thing.
Other than being lectured by some of the best in their field (most notably Mike Green's String Theory lectures - a must for any aspiring String Theorist- while I was there they celebrated his 60th with the EuroString conference held at the Math department. John Schwarz came but I didn't see him) there's also the oppurtunity to meet Europe's next generation of leading mathematics and theoretical physics some of which will probably go on to win the Fields Medals or Nobel Prizes. Attiyah, Chandra, Wiles, Donaldson, Abbus Salam and pretty much all of the British mathematicians and theoretical physicists who've won those prizes all did Part III. So the "networking" oppurtunity is great.
After the first semester, I knew that High Energy wasn't for me because of it's detachment from experiment. I also understood why the String theory groups were so selective in choosing PhD candidates. It's because the problems they work on are really very hard and to commit to the field is actually a VERY big career decision one which you have to make very early in your PhD and requires lots of committment. So they have to look for evidence of great talent, hardwork and dedication (Part III is a good test- it's more like a PhD recruitment programme, which gives anyone a fair chance... just do well in the exams they say) in their applicants to ensure that they won't jeopardize their research career at such an early stage.
Anyway, if you do decide to have the Part III experience remember your ultimate goal... that is the "distinction" grade and work hard to do well in the exams. Most of the questions are usually "book-work" questions. To be fair, they can't possibly ask you to be too creative and original in thinking when doing the exam questions so they mostly ask you to reproduce to lecture notes in these questions. So it is possible and in some cases even necessary to remember answers without understanding them. The PhD students there that i've spoken even to admit that they only truly understood the lecture material in their first few years of their PhD.
Now I've decided that I wanted to work on theoretical condensed matter which still had many unsolved problems (high T-c supercons.) and new phenomena emerging from experiment (BE condensates, fractional statistics) but I didn't regret my Part III experience... in fact I think I learnt a great deal. It's like a freakin buffet of courses to take. The list is just WOW... It's so easy to over-indulge in lecture sitting and so easy to neglect the example sheets and classes. But I learnt that real learning doesn't happen in the lectures... it happens when you take the time to self-study and sit under a tree and figure out what all the scribbles mean. Anyway, I didn't get the prized distinction and had to settle with a Merit because I didn't put in as much work as I should have and there were other distractions as well (WORLD CUP!!!). But I did learn a lot and that's the most important thing... even if it didn't count as much when it came to exam time
The upside is that in the rest of Brittain Part III is highly reputable. Even the theory group at my old Uni takes mostly Part III's and even Goldman Sachs London likes to hire PartIII's.
The other quirky thing about Cambridge are the colleges. You belong to your college first, then your deparment, then the University. It's a weird system to get used to, and one that can sometimes be very unfair. Like if you belong to a rich college you get plenty of perks and otherwise if you don't then... well it sucks. There's also the thing about tradition and dressing up for formal dinners and rowing mania. Oh yeah, it's also cool to see Steven Hawking move in and about the department. To mere mortals like me it just seemed like a surreal world. Cambridge is also very pretty and quint... it's the real deal in my opinion unlike the imitation that they have in Mass. USA.
Anyway all the best. I am applying to the US this year because I didn't bother with the GREs during my year at Cambridge... it would have been suicidal. Hope this reply wasn't too long. Just remembered... Jeff Goldstone also did Part III, he gave one lecture while I was there about broken symmetry... no surprise why.