Hi Eleanor!
I work with schools and a we support a few Classicists from time to time.
The second biggest difference is the obvious one: Oxford is 4 years whereas Cambridge is 3 if you have at least one of full A Level Latin or Ancient Greek (or equivalent).
The biggest difference is Cambridge course is, accordingly, both extensive and intensive in the extreme: the first two years are very tough especially if, say, a student is doing Ancient Greek from scratch. They will need to reach post-A Level standard in Greek in two terms,whilst grappling with significant texts pretty much from day one!