I visited Mada'in Saleh in December 2018 as part of a trip to Saudi Arabia for the inaugural Formula E race hosted in Riyadh. I took a day trip up to Al Oula where our group got permission to visit Mada'in Saleh.
(Mada'in Saleh is currently closed indefinitely for improvements, however, I didn't think the site was actually in that bad of shape. The roads and signs did need some upkeep, but the current conditions were more than passable for visitors. I've seen much worse at other sites around the world).
We had the entire facility to ourselves. There wasn't a single other visitor or staff member on the property that I could see.
The site is most similar to Petra, as it was built by the same people during the same time period. However, the site is much more spread out than Petra is. You can see most everything at Petra with a good day of walking. To get between the sites at Mada'in Saleh, you really need a car.
The biggest difference between the two sites is that Petra was an actual city, whereas Mada'in Saleh is more akin to a graveyard. Almost all of the structures were built as tombs.
The area around Mada'in Saleh is very similar to what you will see in Wadi Rum in Jordan. Southern Jordan and Northern Saudi Arabia can sort of be considered a single geologic region. The Bedouin of Northern Saudi Arabia are similar to the Bedouin in Southern Jordan, it is just that the borderline was drawn between them.
Saudi is quickly opening up their country to tourism, and the Al Oula region is high on their list of tourist destinations they want to develop. Over the next few years, more and more people should be able to visit this site.