In my opinion, it's more Dinosaur /Haunted Mansion / Stitch/ A Bugs Life scary than roller coaster scary. It's not fast, upside down, with drops scary. It's dark animatronic monster scary.
Some kids do fine on wild roller coasters but freak out on a dark ride. Some love dark rides, but freak on coasters.
I actually thought parts of the ride were a little scary. I've never liked my legs hanging down where I can't see what's under them, so knowing there were these big monsters right under me by my feet that I couldn't see kind of made me nervous. Just in a fun way, not a super scary way, though. If your child can handle being alone in the dark while large animatronic monsters attack, they will be fine. However, if A Bugs Life scares them, I wouldn't recommend it.
The scare factors are: (Beware spoilers)
Dark ride
Limited vision, cannot see feet hanging down or what's near you, cannot see parent sitting beside child, cannot see other ride vehicles, only see the HP world around you
Life size animatronic monsters including a dragon, dementors, acromantula (giant spiders), and the whomping willow that chase and or attack you, these monsters sometimes get very close to you, I'd say within a few feet, you actually fly between the whomping willows branches as it tries to smash you
Ride goes through the chamber of secrets
Large dragon on a screen chases you
One of the rooms appears to be collapsing with you in it
Some of the scenes on the screen can be a little intense and cause motion sicknesses
Ride does move swooping up down and side to side, but not upside down (ride movement tame compared to a coaster, more nausea inducing than scary)