At the shows that I have been to it would Border Collies but I think the location does affect it a bit, there are a good number of mix breeds competing in my area.
Border Collies and Border Collie crosses are very popular for obedience.
Then it would be Golden Retrievers (I see a good number of them too), then probably German Shepherds. I see a few heading dog types and other medium sized mixed mutts.
Border Collies (and their crosses) are also the most popular at agility, along with other herding breeds (heading dogs, beardies, huntaways and crosses of those breeds).
If we just look at pure bred Border Collies then I would say there is a definite difference between obedience BC's and agility BC's in both temperament and conformation.
The agility BC's are a lot more hyperactive. Obedience BC's tend to be a lot stockier/heavier framed and usually have a lot more coat whereas agility ones are more wiry and often have less coat. Obedience BC are calmer.
Eg, Based on my limited area this is my observation: Waiting in line for an agility run the BC's are tugging, tugging, tugging while their eyes are darting around at the same time. Some are barking, some are being held back from running into the ring to start the agility before their turn.
Waiting at obedience you will see BC's standing clamly with their owner, watching their owner, doing a little warm up heel work, some tugging, some practicing a short stay, food rewards. There is never barking in the obedience warm-up area in obedience.
It is almost like obedience and agility BC's are completely different breeds (obedience BC's are more like show BC's while agility BC's are more like working BC's).
As for Golden Retrievers. I see a good number of Goldens in obedience. I know of two Goldens that do agility. Again, you see temperamental and conformation differences. The agility Goldens I know look more like working dogs, they have a finer build, less coat, a more golden (darker) colour. The obedience ones are a lot stockier and for some reason tend to be lighter coloured, a lot are pretty much white rather than golden (I guess that is, again, more like show goldens).
For German Shepherds. I've only ever seen one in agility (black, looked working line). They do well in obedience too, I don't think they are as popular in my area though.
Because those are the most popular breeds it makes sence that they would win the most.
If I have a look in the NZKC magazine that I get each month, I'll list the winning breed (this is NZ wide, for one month, all levels of competition including Special Beginner):
Golden, German Shep, Golden, Golden, Golden, German Shep, Swiss White Shepherd, German Shep, Heading Dog, Australian Shep, German Shep, Golden, German Shep, German Shep, Golden, BC, BC, Shetland Sheepdog, Golden, Poodle (Standard), BC, Huntaway cross, HuskyXBC, Shetland Sheepdog, Golden, BC, German Shep, BC, Cocker Spaniel cross, BCX, Belgian Shepherd, BCX, Golden, BC, NZ working dog, BC, BC, Cocker Spaniel, Doberman, German Shep, GoldenXHuntaway, TerrierX, BC, Golden, Golden, Golden, BC, Rhodesian Ridgeback, Heading DogXBeardie, BC, Aussie Cattle dogXNZ Heading dog, BC, Rottweiler, BC, BC........ I think that's enough.
Some of those will be the same dog winning multiple times at the same show or at different shows if they travel a lot, or multiple dogs owned by the same person.
But it looks like it's mostly BC, Goldens, German Sheps and a sprinkling of other breeds.
Hope that helps.