I have been offered a place at to do an LLM at NYU (with the Dean's Award) and Cambridge (UK). I'm from a developing country in Asia and will be specialising in International Law. My prospective career is foreign service. Where do you think I should go?

First of all, both are great for studying international law.

Studying at Cambridge would be rather different from studying at NYU. It's an English university town v. great Metropolis. English lifestyle is also different from American. Which appeals more to you?

You might get more personal attention at Cambridge. I believe Cambridge still offers tutorials. My fellow student at Yale, who went to Oxford, highly praised Oxford tutorials.

Life in Cambridge would probably be idyllic for study, but NY has great cultural attractions. Because the UN headquarters are located there, networking might be easier in the Big Apple.

If you do not receive tuition waiver or other funding from NYU, Cambridge will be significantly cheaper.

My gut feeling is that NYU faculty conducts more cutting-edge research in international. On the other hand, if you goal is international diplomacy, it might not make a huge difference.

Outside the legal circles, a Cambridge pedigree is probably more prestigious. I believe that the best university brands all over the world are Harvard, Oxford, and Cambridge. Perhaps you might want to consult diplomats in your home country, ask them for an opinion.

In sum, if you receive no financial aid, you should opt for Cambridge. It gives you a good education in international law, is cheaper, and is a great brand. On the other hand, if you want to be where the action is, go for the NYU.

My understanding is that Cambridge doesn't have the tutorial system - it is unique to Oxford.
I don't think it is correct that you get more attention at Cambridge. My friends who went there said they were just given a reading list for each course and told to go for it.
My feeling is that they are such completely different experiences that you should know in your gut where you would rather be.

Thanks for the correction regarding tutorials.

If you're main goal is diplomacy, it won't probably make much difference which university you choose. Like Flygirl said, go with your instincts.

I suppose I agree that your choice won't make 'much' of a difference, but, that said, I would go to Cambridge hands down. Better reputation, smaller classes, more exclusive (i.e. harder to get into, and fewer grads) and half the price.
Absent a very big scholarship from NYU or a perhaps a placement at the UN (NYU's proximity might be an advantage in this respect), there's no contest, in my view. And even the UN point is debatable since you could always go to there post Cambridge LLM for one of their many year long internships, which, frankly, would be more usefull for your CV than a part time coop thing while studying at NYU.
None of this is meant as a slight against NYU, which, to be sure, I believe is a terrific institution; it's just not in my view in the same class as Cambridge. If the choice were between, say, LSE and NYU, then it would be tougher.

I can't really speak for Cambridge but at least in the US there is very little focus on EU law or ECHR law which may impact which university you want to study at. There are courses in the US on EU law but it might be more difficult to find many professors interested in EU law in the US.
In the few international law courses I took at both NYU and Columbia I found them to be highly theoretical (drawing on political theory etc) as opposed to "black letter" or doctrinal.

I really think this should be a relatively easy decision. After reading the course websites and figuring out which city you want to live in the schools are so different there must be one you are drawn to more...