Arguably this is a feature request, not a bug. But the binomial coefficients are so important, I'll call it a bug:
Doesn't simplify to zero
(%i255) binomial(a,a-b)-binomial(a,b);
(%o255) binomial(a,a-b)-binomial(a,b)
But makegamma takes care of it:
(%i256) makegamma(%);
(%o256) 0
makefactcan handle it, too