I’ve only seen a couple discussions about this, and they weren’t very informative. With that said, here are my questions:
How competitive is admission for these 2 programs?
When is an ideal time to apply? I'm assuming second semester of sophomore year for Cambridge since Pembroke offers the spring term study abroad, but what about for Oxford?
How is the experience as a whole? I read a little about Oxford study abroad, but I couldn't find much about Cambridge study abroad.
All three of your questions depend a lot on the program you are going through: is it your home university, or through a study abroad program? they will have their own rules / dates and program that will (to some extent) will affect your experience.
My home university doesn’t have a partnership/exchange program set up with both Oxford and Cambridge. I’ll be participating in a study abroad program that will have to be approved by my home university.