What are some of the issues one should keep in mind while choosing between a fully funded offer and another with no funding?
There are four outcomes to your master's program:


You don't complete the program.
You complete the program and can't find a job dependent upon the degree.
You complete the program and get a job dependent upon the degree.
You complete the program and continue in academia.


If you take the position with support, you will be better off in case (1) and (2).  Case (4) is a tie -- you can shift research groups for your Ph.D., and you will be better off financially, but you have to spend 2 years doing things you don't entirely like.  Case (3) is the only case that's a clear win for the no-support degree; you'll have 2 years of chasing your joy, and a fairly small debt that you'll pay off soon in a high-paying field.

What's left is to evaluate the relative probabilities of the four cases.  You need to be objective here, and use the evidence you have: the expert judgement of the graduate programs to which you've applied.  Admittedly two data points is quite few; it would be helpful to know if you applied to other programs, and what those results were.  However, in the opinion of the more prestigious program, you are not one of their best candidates (or else they would offer you support).  

In summary, choosing the no-support program is a large gamble.  You should take it if you're confident that the program made a mistake in not offering you funding -- you have tremendous talent that for some reason has not been revealed in your record.  Absent such a situation you should take the support.  You might change your mind and decide you like that sort of work.