What are some of the issues one should keep in mind while choosing between a fully funded offer and another with no funding? I have been offered a place for a masters program in 2 places. One which is fully funded and another one where there is no aid that has been offered at the time of admission. 

I guess if the everything else was the same between the two then the answer is obvious, which is to go for the funded one. But the problem in my case is this: 
In the fully funded case I have been offered a place in a research group I have no primary interest in (and no previous knowledge of) and something which I would not have definitely chosen if I was given a choice. So in sum, although it comes with a lot of money, the work is something I'm unsure if I will enjoy.

In the second case, there is no aid. The tuition fee + living is something which is not completely unaffordable for, I hope to manage those with loans and some family money. Aside that, I feel there is a lot of flexibility (or at least some flexibility), as I can choose my domain of work and my advisor once I have enrolled, and maybe been through a semester. Also the coursework here is a lot more closer to my preferred area of research. 

Additional info: Comparing the two universities as such, the second one (the one without aid) is higher ranked than the other one (with full funding).

So given all this, how do you think I should make a decision and what is your opinion on the same?

Edit: Both programs are research-based and require a thesis.
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.