I would rather travel with the Doctor because I believe Hogwarts must be out there somewhere and the Doctor can bring me to that. But that in no way means that I love Doctor Who more that Harry Potter. And even if he does leave me, it wil all be worth it and I'm sure he will leave me somewhere incredible, like Hogwarts.
I'd rather go to Hogwarts because every Doctor's companion ends up, at some point, having to leave their family behind. And I could never do that. But otherwise, traveling with the Doctor would, obviously, be absolutely amazing.
I would have to choose travelling with the Doctor. The Doctor always seem so lonely, and if I could alleviate that, well gee I don't know, I guess I would feel good about that.
I too would take magical training over traveling with the Doctor. It's difficult, but Hogwarts & the Potter universe just feel so comfortable... It's a place I've wanted to visit since first reading about them. As much as I enjoy watching the Doctor's world, I don't feel drawn to live in it the same way. Then again, I'm an aspiring educator. The books & the classrooms... I WANT TO GO TO THERE.
Plus, being a companion... That's not a lifelong adventure. It's maybe a couple seasons & then they write you out and you're back to being a normal person. Being a wizard lasts your whole life... ^_^
Hogwarts. Because, although it's not that MUCH safer than traveling with the Doctor, it is a bit safer, and you get to learn fantastical things that I have dreamed about since I was a kid. Like doing so well that Professor Snape can't take away points. Or learning how to turn into a Hippo. Or taking the O.W.L.'s. And the Doctor is fantastic, and he's never boring, and there's no homework, but we don't actually see them LIVING in the T.A.R.D.I.S. How good is the food? How well do they sleep? How comfortable is the toilet? These are all questions that don't have to be asked at Hogwarts, because magic can make even the hardest toilets comfortable. So I choose Hogwarts, because of comfy toilets.
I would rather travel with the Doctor because that way I would get to have more fun while still being the person I am. If I went to Hogwarts I would have to have been a wizard (which I am not), and I wouldn't have gotten the learning experiences I am currently getting at my school. It is really sad when a Harry Potter fan prefers her really strict middle school to Hogwarts. But it is only because I am in a full-time gifted program with teachers that are good at making subjects interesting and keeping the louder students in check. Also, because my favorite subject is history and Professor Binns is a really bad teacher.