University of Washington: Is it worth to apply to the Applied Math Online Degree?

 
I am not sure how being out of the U.S. complicates things, but I'll try to give you some ideas on the two questions you asked.

Some background on me - I went through the computer engineering undergrad (2008) and EE:Systems masters (2010) programs at the University of Michigan.  My thinking is that the quality of a program comes directly from the quality of the faculty in that program.  At Michigan (in both undergrad and grad school), I had absolutely wonderful profs (some of whom I now consider mentors and friends) and I had profs that (in my opinion) should probably not be teaching.  My guess is that most students in most colleges/universities have had a similar experience.  With that out of the way, on to UW.

Your second question is easy so I'll start with that one - the diploma you receive for the AMATH Online Masters program is the same diploma that the on-site students receive.  There is absolutely no difference.  There are drawbacks to being an online student - such as (as of 1 December 2015) not being able to ask questions during a live lecture, and not all courses are offered online.  However, I found that in my case almost all of the courses that I wanted to take are offered online.  I strongly recommend that you check out the list of courses that they offer online and make sure it matches up with your interests.  Also check out the online courses offered by other departments - the aerospace and mechanical engineering departments have many offerings that have an applied math flavor.  Also, online students are permitted to take independent study with a prof, so you could try that to cover some material for a class that is not offered online, but YMMV with the prof and whatever is on their plate that quarter.

Now to your first question - I can really only compare it to the program I was in at Michigan (which was a very good program, in my humble opinion).  I will also only compare the quality of instruction since I consider that the most important aspect of an online masters program - but that is a completely subjective measure, so take what I say with big grain of salt.

Quality of Instruction
I started the program last Autumn quarter and I have been very impressed with the quality of instruction in the AMATH Online Masters program.  As with most educational endeavors, you usually get out of it what you put into it.  Not every professor will always give clear lectures, but if you prepare a bit before watching and ask the TA/prof your questions you will be just fine.  Part of the instruction in the AMATH courses is the online discussion board where you can ask the other students in the class your questions (including the on-site students).  This helped me a bit from time to time, and I also was able to answer a few questions for some other students.  It is definitely a plus.  

Overall, I would say that the quality of instruction is slightly better than what I had at Michigan, but not by a wide margin.  

Hope this helped.