There are several differences you can expect from one EQ implementation to another.
There are two main types of Q interpretation: constant Q and proportional Q, you will see the difference explained page 4
here. This is the most important source of audible difference you can expect, and one that should certainly not be ignored.
Another (lesser) difference will be the behavior in high frequencies, as cramping will happen when approaching Nyquist with many implementations. So the response in HF might vary depending on the sampling frequency as well as from one implementation to another depending on the way this cramping phenomenon is handled. You can read more about this
here.
These two differences are linear distortion, but you also have non linear distortion that will happen with IIR due to quantization errors, especially in the low frequencies, and especially with 32 bit implementations (most hardware ones). This might look innocuous at first but these errors do add up, and there are worse case scenarios, even with 64 bit implementations.