Um... that really depends. If you have an algorithm that is numerically unstable, these errors will quickly lead to a completely wrong result. Using a different type is not going to fix that, of course, and you need to fix the algorithm.
However, even though algorithm A and B are "correct" they can behave differently when rounding errors are introduced.
For example – if algorithm A uses
and B uses naive summation then you can expect the end result of A to be more precise than the end result of B – even though both algorithms are correct.