I actually find mid-to-late July less busy compared to when we usually travel to Disney. We travel at some of the busiest times of the year (Easter, Thanksgiving, have done other big holidays as well), and in comparison, July feels like low crowds to us!
To answer the original question, I find they’re both accurate. I used Touring Plans recently for our spring break trip. Don’t rely too heavily on crowd calendars, though. We pick which park we want to visit on different days. If it happens to match up with what a crowd calendar claims has lower crowds, great, if not, we don’t worry about it. One thing I’ve found is that parks can be busier during days with EMH, so if it’s possible for you to do a different park on those days (unless you want to use the EMH), you might want to try doing that. If it just doesn’t work for you, though, don’t worry about it too much.