I really do not think it makes a difference. For undergraduate school, you may have a hard time making friends, catching up with the curriculum with your peers, modifying your educational plans, etc. even though a lot of people apply for the Spring because of their personal circumstances. But for graduate school, your candidacy is more important.

Universities usually have a limit of how many students they want to admit for a program based on their resources. These factors could be their capacity, their available professors, facilities, and what not. These factors are important but don’t affect your candidacy. If they really have limited resources they will have a different admission cycle, depending on the programs. Full time programs are normally more structured and you only have one choice.

If you’re planning to get an internship in the summer, however, consider applying for the fall because it gives you enough time to adapt and search. And you have to enroll for at least two semesters (or quarters) in order to be qualified to work.