What separates Oxbridge personal statements from other university applications?

Oxbridge seek to admit people that will do well in an environment that is extremely stressful, academically intense (a LOT of reading), and driven by competition (you need to be passionate about and good at what you're applying for). You'll need plenty of evidence that demonstrates this. Quoting books you've read and essays you've written will be more of a focal point than any practical expertise you have. Oxbridge want academics, not professionals. Moreover, in the interviews, personal statements do not matter as much, although they will ask you about them. You need to demonstrate academic ability and passionate interest that enable you to not give up half-way through your degree and keep fighting through extensive reading lists in your personal statement. You will have to do some reading for your personal statement, if you haven't already. I can make individual recommendations about what to read and how to employ that reading correctly, if necessary.