I personally think conures bite harder and have more of a chance of frightening a four year old, but, really, it all actually depends totally on the individual birds. When my sons were little we had both a cockatiel and a dusky conure, and neither bird ever bit either boy, so there you go. However, it doesn't take but a couple of bites to keep most kids from interacting with a bird.
I could never consider owning a sun because, like Jenny, I can't tolerate their calls - not at all. I can tolerate pyhhruah conures with no problem, and I never had an issue with the dusky, but she didn't scream, either. I've heard other dusky owners say their birds were both loud and mean.
I have to say that the bird store I freqent almost always has a sun conure in there that someone returned because they couldn't handle the noise. It seems as soon as one finds a home, or even before, another returns. This doesn't mean you and your daughter can't handle the noise, because people who love suns can't live without them. The bird store sells lots of suns, so really only a small percentage are rehomed. They are big sellers. They always have greys being rehomed in there, too, and probably because, as far as I can see, they sell more greys than any other type of bird.
Cockatiels can be annoyingly loud, too, so do spend a lot of time in the company of both making their loudest possible noises if you have the chance.
Other than that, pick the bird you fall in love with.
Please understand the individual birds personalities make all the difference in the world, though, when it comes to gentle behaviors. I have 3 kids, one had a dusky conure that never bit him, one had a cockatiel that never bit him and now has a linnie that also has never bitten a soul, and one has a bourkes that has never bitten.
Best of luck in your search, and have a joyful experience with your daughter and your new companion.
