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German has a perfect response "jaein." I guess the translation (there is no real translation) is "yeah, but no." The program is only 5 years old and is starting to have students apply and enter some of the top European PhD programs, which has helped create a touch of awareness for the program in the US. Name recognition is on the rise, but it still has a way to go before it becomes a "premier program." This is partially due to the German education system and culture around graduate programs. In Germany (generally Europe too), graduate programs are seen as a means to weed out researchers and scholars from professionals. This leads the university, staff, and professors not offering much help unless you reach out and ask for it. Even then, you must be prepared or you will be brushed off. The idea, from my experience, is to throw students into the deep end and see who swims and who floats. The floaters are passed through the program while the swimmers are fine-tuned and prepared for PhD study.
I recommend picking up German if you study in Germany or do anything related to Europe since most universities will ask you to have basic knowledge of German for advanced studies. In the case of the MA in Berlin, German is an unwritten necessity. You can complete the entire program in English, but you will miss out on the uniqueness of German academia and historical thinking without a working knowledge of German. Since I am training to be a historian of Germany since 1945, I loved my experience in Berlin as it taught me a lot of important realities/effects of the Cold War ('the West' and 'the East' blended in a curious manner in Berlin after 1990). If you are training in African or Chinese history, then I highly recommend the program as several renowned European scholars work in Berlin and the program encourages outreach to these scholars.
Lastly, the student body is a mixture of 'good' and 'bad' students. As stated above, the system will not babysit you. A lot of American and British students expect the system to support them by holding their hand due to the design and goal of American and British undergraduate systems. The German system is a sink or swim one and it is ruthless, which, I believe, has caused mixed reviews of the program. If you are studying an MA to prepare for a PhD program, then you will not have any problems in finding support. If you are studying an MA to live in Berlin, however, then be prepared to flounder.

I admit that I may have a bias! 
 

Here's the thing...most MAs in the US want students so they can get our money. Sad, but true. You should definitely apply and focus on your statement of purpose over your grades. If you had an "off" quarter, explain it in the least "woe is me" way possible (for example, I went through a period of low grades then turned it around, but during my low period I had a baby--not that it excuses the grades, but it was a way to show the committee life happened). Otherwise, get strong recommendations, write a stellar SOP and polish the f--- out of your writing sample.
If I was you, I would look for world history/South Asia scholars you admire and research their programs, not the other way around. Maybe these scholars' departments offer general history MAs but have a good cohort of people in or related to your field. That way you won't be as limited in where you consider. There's a fair chance many of the historians you've read work at M1/M2/M3 universities (majority MA granting)...it's just a fact of the job market.
Good luck!

Neither one of these are good choices, frankly. The MAPH/MAPSS program is very much a cash cow, cut throat MA program. I've met several graduate students who went through that program. None of them impressed me, beyond the degree they were cutthroat ladder climbers, some of the least pleasant people I've met in graduate school. The Columbia MAs are very well-known for ignoring their students and extracting as much money as they can from them. 
 

The MAPSS is very different from the MAPH both in terms of environment and student outcomes. There's usually at least half tuition covered, and they have a solid placement rate both within Chicago and elsewhere. I've known many very nice MAPSS alums, including at least two in my current program. Of course, Chicago in general tends to breed a certain type of... how to put this nicely?... aggressive student, but those who did their undergraduates there are usually the worst offenders.

You're at GWU, a research university with PhD programs in both Political Science and History departments.  You would do well to speak with your professors both in those departments.  They can best guide you to choose your disciplinary focus.  
Your GPA is fine.  Just apply.  But I'd really recommend taking a year off after those 1-year MAs so you can present a finish thesis for a writing sample.

I can assure you that your GPA will be the least important thing in your admissions decisions. I think you stand a really good chance if you can showcase how your major in Economics and International Affairs has influenced you to become interested in obtaining an advanced degree in History. Best of luck!

@TMP  Never applied, hence my silence.

I heavily encourage you to look into 2 year MA programs in History or in a subfield of history that you're most interested in. There are a number of reasons I'd recommend a 2 year program over a 1 year program:
2 years will allow you to gain a better understanding of your interest and discover new interests that you may never knew existed. This will allow you to gain more time to present at conferences in your field Two years also allows your professors to know you more and encourage you to submit to conferences in your field that you may not have been aware from. Grad schools might also have funding set aside that you can apply for so you can present at such conferences This will allow you to take a full year of courses to figure out who you could ask to write your letters of recommendation If your ultimate goal is to obtain a PHD in the USA, professors in the USA are more accustomed to the PHD process here. While the job market remains rough, it's easier to land a tenure-track job if it's from the same country you graduated from

Have you looked into MA programs inside the USA that are funded? Being in a funded program will allow you to focus on your application for the PHD without having to worry about finances for moving countries, living expenses and such.