I'll look at this from as many angles as I can. Of course, I'll still be biased as I'm a uni student myself who's looking to tutor students, but here it goes.
Advantages:
Uni students have done the courses relatively recently, and if they're studying that field at uni, they might understand the material better than a high school teacher who only remembers the course content. If not, they'll still remember what they did to succeed in the given subject
Uni students are only a little older than you, compared to adults, so it's easier for them to relate to your struggles. Arguably easier to befriend a uni student tutor than a 40 year old tutor I think.
They really want to keep students as for some of them, it's their only source of income. So they sure as hell will try and keep their students
Disadvantages:
Uni students can be busy, yes. Not just with uni work, but with other commitments like sport, other jobs, hanging out with friends etc. Plus, they're known to procrastinate (I am SO guilty of that) so they may have to juggle priorities
It can be hard to tell if a uni student is just out for your money, but that's a risk you'll have to take with anyone.
Not all uni students will be happy to compromise on location as they may be busy; this could make things really inconvenient for you, and this is just something you'll have to sort out on a case-by-case basis
Uni students generally don't have formal training in education, although this is somewhat mitigated by the fact that they're just teaching material they learned a few years ago
I have tried to be objective here, but nevertheless there may be snippets of bias here and there because of my standing as a uni student.