I think a lot depends on how and where you go about finding the man you are inviting into your sex life.
If you look for a "dominant bull for a cuckold couple" you will attract those who are more into the humiliation aspects inherent to that type of scenario.
Whereas, if you look for an "attractive, well endowed man to join a married couple for an evening of pleasure", you will probably get a different type of man responding.
Additionally, how you dress and the sort of vibe that you give will differ relatively as well, especially how the husband conducts himself. If he comes across as self assured, the "bull" will react accordingly, just as if the husband projects being submissive or even "wimpy".