Hey just going off what @leftandaright says, with whom I agree.
Academically I feel Oundle has a higher top end - top 20/30% might be more naturally smart than Rugby but this is subjective. Middle and bottom will be the same. Support at both v. good.
Neither are ridiculously selective, hot-house academic schools but for the more academically capable all rounders. Oundle only do A Levels and SATs. Rugby do this as well as the IB. Oundle has an off curriculum course which is cool called Trivium and Quadrivium started year after I left. Not sure about Rugby.
Music is stellar at Oundle; it is paired with the Royal College of Music so support from their professors etc. I am sure Rugby's is great too. Difficult to compare music, likely same amount of opportunities and support from grade 3 flute to wanting to go pro.
Oundle is huge so is never scrambling to fill spaces in anything in my experience: orchestras, plays, sports teams, societies. I liked that about the school, it really allowed you to do what you like and not force you into anything (bit like Eton in that way), and due to size you'll likely find others interested in something even the more off-grid things. If it's not on the cirriculum, they will put it on (we had a tapas and tertulia society started when I was there).
Student amount-wise:
Oundle 850 Full boarding, 250/300 day
Rugby 650 full, 200 day.
I'd go with your gut. It was between Oundle, Marlborough and Rugby and we liked Oundle town more, the "vibe" and it was a closer to home and didn't feel the need to travel to Rugby or Marl. But Im sure I would have done well at the other two and loved my experience.
Good luck