That's an interesting project. I think because of the differences it will show up more than what are generally superficial similarities. But that's useful too.
On similarities I'd say that One Direction does seem to have that charismatic element to them that makes people want to like them. This was a very big part of the Beatles appeal that is now sometimes overlooked. I don't know a lot about One Direction but when they came to Australia they did come across as nice guys who convey their enjoyment with what they do.
Normandie has pointed out a lot of the key differences. One area that is perhaps worth exploring is the difference in musical upbringing that pop musicians of the Beatles era experienced compared to the modern era.
When the Beatles were growing up there wasn't the proliferation of teachers, resources and courses to train aspiring popular musicians. They were mostly if not entirely self taught, usually on third rate instruments. There's a cute story in the Anthology series of Paul McCartney and friends getting on a bus across town to see someone who could show them a B7 guitar chord.
Again, not knowing the One Direction chaps specifically, but I'd be very surprised if they all hadn't had, from fairly young ages, voice training, been taught instruments and/or been on specific courses to teach them popular music. If they're like my daughter and were learning instruments they'd have access to good quality instruments, teachers of multiple styles and online resources to find chord charts and tablatures for songs they wanted to play. Unlike in the Beatles day, being a pop musician is almost seen as a potential career for which you train; like any other profession. Even the fact you're doing a school project on this is an indication of the difference in the eras.
That's my two cents worth. Good luck with it and enjoy.