Sorry not meaning to sound snarky at all. I really am not kidding when I say I cannot to to a dog event without someone telling me how papillons are little border collies and its just not true. Yes they are more biddable than most dogs. Yes they are super handler oriented. Yes they are seen and excelling a lot more often than most toy dogs in performance rings. Yes they tend to be med- high energy. But not border collies.
I adore both breeds and know many people that do and own both. I've also met a handful of people that don't like both.
I think in general with sports you need to pick a dog you like and enjoy vs one that will just do well. I mean... Sports are a consideration but not the whole picture or even the main one for most people. I wouldn't focus on which breed is 'best' at a sport. Just if they would enjoy your lifestyle (sports being a part of that) and if you like and enjoy the breed.
If you do have any papillon questions ask away.
Eta: I do realize why people compare the two and that it is meant as a compliment. I have a hard time accurately describing paps sometimes. They do typically have a real desire to work and do things that you don't always see in other toy dogs. Too many people see a cute fluffy little dog and assume low energy and not much work, which isn't my experience. They can be very adaptable but they will very much enjoy more activity and work. I am still often wowed by how a sweet little dog like Summer really can turn it on for agility.
Ack long posts.