This is a question I've had to answer a few times since making my decision, since I also got into two very good programs in the US. I've also had a few conversations about the reality of studying in the UK with some of my college friends and why I think it can be a better fit for some students.
1.) MONEY. Rather, value for money.
This is one of the biggest considerations about going into grad school for many students. I know it was for me. Especially for the humanities, there are very few fellowships or fully funded programs available in the US of A. Not that British programs necessarily provide you with more funding, but I'm pretty sure the math works out (in most cases) that it will be cheaper and FASTER, making the cost per credit less. Nearly every Master's program I saw was a year long program, and when I say a year, I mean a full 12 months of classes/work/experiences, not the nine months most American programs run.
For example, the Master's program I was considering in America was two years (or three, depending on if you did a dual degree, which I intended to complete). The tuition was $965 per credit hour, for two or three years, for nine months of classes. There were not any fellowships available for this coming year, just a part time on campus job for $12 an hour. This was in no way going to cover tuition, living costs of a big city, or supplies for classes. My UK university costs £13,500 for the entire year of tuition. This includes two semesters of full course loads, an internship or elective component, a field-study trip to Europe, and dissertation advising through the summer. I will have another degree in 12 months, along with experiential learning. It's pretty great. (FYI: The cost of living in Glasgow is a wash with living in Chicago.)
The kicker, though, is the length for a Ph.D. program. The majority take THREE YEARS to complete (you have to have done a Master's first). That's four years total to get a Ph.D. That is pretty much unheard of in the USA, where it takes at least five years for a Ph.D., if not longer. So yeah, saving time and money on further education seems like a great idea!
There are also scholarships available. There are the super competitive ones- like the Marshall, Rhodes, etc.- or specialized ones, like the St. Andrew's Society of the State of New York, for which I was a finalist (seriously one of the coolest experiences, even though I didn't receive it). British universities often have their own scholarships for international students or specific programs as well, so there is definitely a way to find outside sources for money. I will (probably) have to take out a loan as well, although the FAFSA can apply to Glasgow, so that's convenient. (I wish American student loans worked like British ones, but that's a post for another time). At the end of the day, I'm taking out a smaller loan than if I went to school in Chicago, and that's what really matters- I'd rather go broke doing a program I really love and traveling than spending more time in school in a country I've lived in for 22 years. (I know this is my opinion, but it's obviously something to take into consideration)
2.) SPECIALISATION
I also think there are far more specialized Masters programs in the UK, across the board. Obviously I haven't looked into this too much for disciplines outside of history, art history, and archaeology, but I have heard similar observations from people in the sciences. There are also unique programs you can't find in America-- I'm the poster child for that. In a way, this can save you time by taking classes exactly pertinent to your interests or speciality. However, there are also good survey programs as well, which can help you figure out what to focus on for further research and study or for you career. My program is a combination of these two aspects, which is what I really love about it.
A thing to note about British post grad courses: there are two types, taught and research degrees. Taught degrees (always a Master's program, never a Ph.D.) include classes and what we normally associate with the first few years of grad school. Research programs are exactly what they sound like: you complete a research project with some level of advising, but you're pretty independent. Most undergraduate programs in the UK require some form of dissertation (not anything on the level of Wooster's I.S., but more than many senior capstones across the US), so this kind of research isn't necessarily new to all students on the other side of the pond, and Master's programs also require a thesis (ALSO shorter than my I.S., I might add, but Wooster's an odd egg on occasion). So bear that in mind when looking at programs and exploring your options. And DO explore your options- there are more unis out there than Cambridge and Oxford, and many specialize in unique departments. For example, Glasgow is the top art history department in the UK, and York has a killer archaeology program. Just because you haven't heard of it in America doesn't mean it's not a high global standard degree! And these schools have been at it for literally centuries, so they have extensive libraries, archives, museums, and access to some really amazing local sites, no matter what discipline you're entering.
3.) TRAVELING
Finally, I think everyone should travel. There is so, so much value to those experiences beyond whatever the price tag for a piece of paper is. If you're leaving home, but not yet entering the work force, I think this is a great time to do it. Obviously there will be a lot of adjusting from undergrad to grad school, so keep in mind if you can handle that and being in a different country (although the UK does- generally- speak English). There is so much out there for people to see, and different countries have different approaches to research, education, medicine, and politics, which can be really valuable, eye-opening lessons before you enter the workforce in your given field. And traveling is a life changing experience to begin with. Once you begin your real world job after getting a degree, you generally won't have the kind of travel opportunities and flexibility you have during school. Studying abroad is like YOLO with an investment and actual worth to your future.
Obviously this is all my somewhat biased opinion, and I am speaking from a humanities perspective. Many science programs in the US will provide funding and living stipends, so the expense of graduate study is not as hard to bear. However, these are just factors to keep in mind, and they explain part of why I personally chose to study in Scotland. This is also my view from America, we'll see how I feel after a few months of Scottish education :)
So now I'm free of my undergraduate obligations and can relax for a few weeks until I start working at Interlochen Arts Camp as a cabin counselor for the third time! After that, I'll have a few weeks to prepare for my year in Scotland, and then I'll be off in the first week of September. It's all very exciting, but it seems much further away than it really is.