Nowadays most languages have some kind of support for arbitrary length numbers, natively on the language or via some external library (i.e. gmp).
The only important difference* is the level of integration within the language. For instance, in C++, Python, Perl, SWI-Prolog, Haskell, C#, etc., big-ints can be manipulated as any other built-in numeric type using the standard math operators. On the other hand in languages not supporting operator overloading as C, Objective-C, Java, etc. you have to use the library functions explicitly.
Depending on the pervasiveness of big-int operations on your application it may pay off to switch to a more big-int friendly language or not.
update
[*] well, obviously, correctness and speed also matter. But, as most languages use GMP under the hood, there shouldn't be mayor differences in that regard. Maybe math-oriented (and expensive!) languages/applications as Mathematica or Maple providing their own big-int implementations can have some advantage here.