I understand that the terms Cum Laude and With Honors are interchangeable, but which one is better understood in US and more commonly used?
Both forms are well understood by people who care about such matters. You are free to use either.
Still, it is the diploma-granting institution (college or university) that decides whether to use English or Latin. My own baccalaureate was awarded "with highest distinction" — not summa cum laude. If you can find out what words were on the actual diploma, use those. If not, it doesn't much matter.
There are some differences in usage. I have never heard a graduate degree being awarded With Honors. "Honors" is for me usually associated with a minimum grade point average (quantitative measure) and "[Summa] Cum Laude" being a discretionary, qualitative measure decided on a case-by-case basis, although it could be based on numbers as well. In this I agree with Dorian:
Most master's programs do not have an honors degree. Since the minimum GPA for maintaining enrollment is a 3.0, there's not such a range of high and low grades, making high scorers the average instead of the exception. Everyone is expected to make good grades in grad school.