From what I know (Our neighbor had Corgis, and I have met several on farms, and at dog shows (Agility), and I have owned Border Collies, and have met them in dog shows also (Once again, Agility. I am not into the "Show" animals).
Corgis are loud, they are funny, they don't listen very well, they have a mind of their own. They love their owners, but they don't know the deff. of owner (They seem to have more of a "This here is my close friend, they feed me, they talk to me, and they provide me with shelter, I own the show" attitude from what I have seen, once again tho, I have not really been around a LOT of Corgis, yes I have met several (Probably around 20 or 30), but have not been around as many as Border Collies.
Border Collies are beautiful, they are also funny (Unless it is trained/bred out of them) (I had one who would sit under a picnic table when it rained so that she could catch the rain, and when it snowed she would shove the snow up with her snout so she could catch it. The dogs we have right now will tip the food dish over, and then pick up the food and put it back it the dish), they love to work (No matter the job), they learn easy and fast, and they tend to have a "This here is my boss, I work for room and board, but I have such a nice boss that he(Or she) gives me treats, even when I probably don't need them! And he(Or she) pets me to! And I love it when he(Or she) talks to me about his(Or her) problems, makes me feel trusted!" attitude.
Once again, I have had a lot less experience with Corgis than Border Collies tho.
Also, I HAVE seen some Border Collies who had the "I run the show, this here is my friend" attitude, but very few, and far between, and the ones I have seen that were like that were dogs who had owners that thought they were raising a prince/princess or something obviously, as the dog was treated as ABOVE them-selfs, and their friends/family!