What is the sending speed with Pro?

The sending speed depends only of your internet connection

On Smash Pro, transfers don't have priority, contrary to the free version.

Concretely, this means that once the loading is finished, they are available for download immediately. There is no waiting time, nor any delay between sending and receiving by the recipient.
That's why we can say your transfers made with Smash Pro are faster. But the speed of loading and therefore uploading is only linked to your internet connection.