Engineering physics is another way of saying applied physics, it's typically part of engineering department. They call it engineering physics to have the program a part of the ABET accreditation scheme, although the programs can vary immensely between schools. Some programs are more like an engineering (EE ME CE) program with a minor in physics, while others are like a BS in physics with a minor in some field of engineering.
If you want to go to graduate school for applied physics, then engineering physics is the degree to seek. If you want to go to graduate school for physics, then it's really dependent on the EP program if you'd be adequately prepared or not. As an aside, it's always easier to go to graduate school in the program you got your bachelors in, so if you know you want to go to graduate school for physics, then get a physics bachelors.
The engineering physics degree would be more employable as a terminal bachelors, although no employer is actively seeking EP majors (or even know what they are more often than not). You'd be able to apply to jobs that specified entry level engineers that some of your course work covered. You could do the same with a bachelors in physics, but with much less success.