Read the course descriptions to decide what you want to do, although they sound the same you'll find what is actually taught is quite different between the same named degrees across universities yet alone between different named courses.
Bioengineering and biotechnology are more biology based in general than the biomed eng. However at some uni's biomed eng is very biology based and actually the same as bioengineering at other uni's. However the majority of uni's teach biomed eng with the same general first 2 years across all engineering courses with a few biology based modules. Just read and chose the one you want to do in the place you want to do it.