First, that guy with the long bow is about as slow as you can be. A skilled Long Bow shooter can have 3 arrows in the sky at the same time, obviously at a distant target. This guy could have never achieved that. Even then, the crossbow was half as slow as the long bow.
The only person who should use a crossbow is someone who can't use a regular bow.
Ordinary people don't shoot like Legolas. The guy in the video was a little slow, but he was still pulling off about one shot every five seconds. The best that most people with training can expect is about one shot every three seconds. That is the fastest speed anyone in my college archery class could muster with any degree of accuracy. Now consider that the longbow in the video was a 110 pound draw (although it didn't look like it, that is what the crossbowman said) and most practice bows are going to be about half of that or less, and I think the old guy with the longbow was doing pretty good, assuming his shots were accurate.
But yeah, figure a very strong and talented longboman might increase the fire rate from 10 arrows per minute to about 15 arrows per minute and if you have a heavier draw crossbow that uses a winch draw, the rate of fire is going to go down from 6 per minute to maybe three per minute and you have a big diffference in fire rate.
Where I see a crossbow coming in handy in TES is for sneak shots against armored enemies or for melee opponents to get off one quick and powerful shot as they close the distance.