My advice would be not to overindex too hard on what your career will be or a ‘specialization’ in psychology. Most good psychology departments offer most of the basics anyway, and the basics are really what you need as a foundation for thinking about a career in psychology or any other field. Specializing is for graduate school.
That said, both Drexel and Villanova offer a perfectly good education in the basics of psychology that could prepare you for any kind of career in psychology. Drexel’s is definitely more technical-leaning and more concentrated in the life/physical sciences: the major requires you to take a life or physical sciences sequence; a two-semester intro to psych sequence; a choice among personality, sccial, or developmental psych (pick two); and then courses in statistics, psychometrics (psychological testing) and data analysis, psychological research, psychology of learning, physiological/biological psychology, abnormal psychology, history and systems of psych, and cognitive psychology. It’s pretty standard fare, although most universities don’t require you to take the last four - they usually offer them as electives you can take.
Villanova offers a very similar curriculum - in the BS, you also complete intro psych, statistics and research methods, and some life/physical sciences classes (biology, statistics, math). The difference is at Villanova you have more choice in which psychology courses you take - you have to take five foundations courses, including two with labs, which does end up meaning you functionally have to take biological psychology and cognitive psychology since they are the only two foundations courses with labs. Then you can choose three out of perception and/or developmental, social, abnormal, clinical, or personality psych, and an additional three can be other electives like cross-cultural psychology, industrial/organizational psychology, human factors, animal learning or psychological measurement. In the BA, you can take one fewer foundations course (and you only have to take one lab course), and you don’t have to take the science courses. Both of these give you more flexibility in building your own area of interest/concentration.
If I had to offer an opinion, I’d say that Villanova is probably better academically than Drexel to some degree. But they both have unique elements to recommend them. One of my colleagues on my team went to Drexel for undergrad. She enjoyed her co-op, and it led her to her first job in the industry.
Also, a note about careers. It’s true that you cannot practice with the title “psychologist” without a PhD, but it’s not really true that you can’t do research or clinical practice without a doctorate. There are many practicing therapists who have a master’s degree; there are several master’s degree programs that will lead to licensure to practice as a therapist or counselor in all 50 states. There are also lots of people doing research - public and private sector, at all kinds of companies - with master’s degrees. Even with academia, there are lots of people who conduct research with a master’s degree, although the ceiling is a lot lower. You can’t do research as a lead investigator in a university setting with a master’s degree, though; that is true.