Well, I would have to say that it depends on how old the dogs are and how well they are socialized.
I have two basset hounds, two king Charles cavilers and a beagle mix. The bassets love everyone and every thing that comes their way. The cavilers are somewhat afraid of the bassets.
So, the basset will probably have no problem with the border collie, but consider this dynamic: A border collie is probable the most intelligent dog breed. The basset (despite the misconception that they are dumb) are extremely smart. The problem is that they are intelligent in very different ways. Bassets manipulate humans and other creatures to get what they want. Border collies are easily trained and do what humans want.
Bassets are an in your face dogs that says “love me”. Border collies are more reserved. A little bit of a clash there but I believe that they will probably end up being best friends. Probably like the odd couple where the Basset will be Oscar Madison and the Border collie will be Felix Unger