Yes, HDD is now just plain too slow. That said, there are even different classes of both HDD & SSD. But HDD shouldn't be used for anything but backup (and not in a RAID on a server unless it is a home media server). As far as the different classes of SSD go, I really wouldn't worry about that as much as getting quality drives. In other words, a good, reliable brand.
Now what is a good reliable brand is sort of an issue. I am going on experience, mostly from the reliability I enjoyed (or did not get) which I experienced with HDD drives as far as quality goes, with Samsung interjecting some superiority because of all the great reviews. However, when you go to buy an SSD, often the newer stuff is not only faster, but also much more inexpensive, just because they get better at making them, miniaturize components and make them cheaper. You can see this on Amazon, the older SSDs are often more expensive. So, if a web host reveals that they are using $400 1TB drives, it doesn't necessarily speak to the quality of a drive unless they reveal the class. Still, NOC or Webserver drives are supposed to be better, but you are reaching a plateau where the higher investment yields fewer returns in advantages.