Not a current undergraduate but given my interview was only a month or so ago I think I can probably help you.
Firstly, let's talk about the courses. You're more limited at Oxford than Cambridge; you can't pick and choose between two many other papers (e.g. politics or classics etc.) because you're expected to pick between Modern History, Ancient and Modern History or History (Modern) and Politics. Sadly the two that give you more bredth have a much more difficult entrance percentages (15% I believe, 30% for the general history).
That to me was the big negative. I'm picking my papers now for Cambridge, and have a choice between stuff going all the way back to 800BC to the present day, which is pretty exciting. Have a look at the papers on offer here:
http://www.hist.cam.ac.uk/undergraduate/part1/index.htmlAs you can tell, you can make it as 'new' or 'old' as you wish. I will be doing the most modern British History and British Social/Economic papers but be mixing that most likely with the European History paper which is 31AD-800AD, which other than a spot of Augustus which I did in Classic Civ is largely new. I won't explain the whole choosing paper system to you, but I can tell you there is lots of choice particularly in your final year (Part II).
Oxford I know less about, just know from dismissing it last year. However, be aware that Cambridge remains A*AA; Oxford I believe will not be requesting A* for your year, so lucky you; if you feel you won't match the A* then bear that in mind.
This person who you compete against might get better grades, but who loves history more? Which one of you will do better in independent study, who will react to new ideas better? Don't really bother to compare yourself to other people. Although saying that I was pretty much the only Oxbridge level candidate in my school for history, but my school's not that great so hard to tell. Basically, don't worry.
Extracurricular largely doesn't matter. I mentioned debating society which I helped run in my old school and my school magazine, but they don't really care. Show that you're a normal human being, and then talk about your love of history and nothing more in your personal statement; it's three things all put together: how you found history, how history found you, and why everyone should have history. That's basically your entire personal statement, with the odd example of particular interests.
The interviews aren't scary, they're incredible fun. I walked in, they were so nice, my first one I came out of so buzzing about what I discussed and exploring new ideas. No one can divulge individual questions, but the majority of the stuff was off the essays I'd submitted and general history questions such as the best way to write history, where to base oneself, how far one can eliminate bias etc. etc.
Further reading is YOUR choice, no one elses. However, the philosophy of history needs to be an important consideration. If you're completely new to this, Josh Tosh's The Pursuit of History is like a textbook which is the perfect beginners guide to knowing your cultural history from your intellectual history; your historicism from your postmodernism. All very important. In Defence of History and What is History? are seen as standard texts that many people have read which would be interesting. I fell in love with Marc Bloth's The Historian's Craft. I made reference to Bloch in my interview.
Try to go off the beaten path a bit. My interest was the British Empire, particularly its effect on Britain itself; I chose a more academic, not general book. That would be an interesting one. Political history 1700s onwards is an incredibly wide subject that has within it thousands of different subgroups let alone which country or decade you're examining.
If you need any personal advice like personal statements or interview prep give me a pm sometime. If you can be a bit more exact about any areas in history, I can try and be more exact with recommendations of what to read. I read around 11 or 12 books before my interview for various things I mentioned or wanted to mention.
Visit both, and go off the feel of the place itself. Do you want a reasonably large city with a city feel (Oxford) or a smaller city that is more campusy (Cambridge). Do you mind not being able to explore earlier History? If not, Cambridge may well be your place.
EDIT: I see someone from the other place has commented haha. HAT I'd argue is actually the complete other way around; Cambridge isn't more grade focussed given they considerably interview more people, the HAT can still be heavily prepared for in a way that the interview cannot is a fairer test. Not having the HAT was to me a significant advantage of applying to Cambridge. Also...
http://www.topuniversities.com/university-rankings/world-university-rankings cough