We will be there at some point over Christmas (December 20 - Jan. 3) What would you suggest is the better option for one day for a 9 year old girl? She is a big Shrek and Despicable Me fan. She used to love Dr. Seuss but not so much anymore, except probably the Grinch. She is getting braver but I don't know how much the big thrill rides will appeal to her. I don't know nearly as much about US/IOA as I do about Disney but we want to check it out. Or should we skip US/IOA and just do a day at HS at WDW?
I think your best bet would be a hopper and just do the non thrill rides and shows from each park.
If you can't do that then I guess US would be best, but only because it will be Christmas time and you said she's getting over Dr. Seuss.
Here's what's available at each park she might like. I excluded roller coasters, thrill rides, or shows with scary or more adult themes like Terminator.
US:
Despicable Me and Shrek are side by side.
There is a very good live animal show.
Harry Potter will be open.
There is the ET ride; it's kind of like Peter Pan.
There is a kiddy coaster, similar to barnstormer.
The Twister and Disaster attractions may or may not interest her, but shouldn't scare her, unless she frightens easily.
MIB is like Buzz Lightyear, but may or not scare a 9 year old.
There is a Simpson's Dumbo like ride.
The Macy's Christmas parade will be running as well.
Transformers is hit or miss for that age. It's intense, but not roller coaster scary. It doesn't move like a roller coaster. Its more the scenes around you, things popping out, heat from flames, scary robots fighting, blowing stuff up.
IOA:
Seussville which is taken over by the Grinch for Christmas
- Cat in the Hat ride = WTP with more spinning
- Trolley Train = People Mover with more to look at
- Carousel
- One Fish a Two Fish = Dumbo + water spraying in your face
HP area
- Kiddy coaster
- Forbidden Journey, more intense dark HP ride, be warned lots of scary monsters here, but the ride movement isn't wild, also child can't see parent sitting next to them
There are a bunch of water/ boat rides that get you soaked at IOA. May or may not be too cold for that at Christmas.
Storm Force = tea cups
Dr. Doom Free fall = tame version of a ToT, looks intimidating but is fairly tame once you are on it
Sinbad Stunt Show
Spider-Man - pretty much same as Transformers just different thing, a little less intense, but could still be considered scary by some kids.
You will also want to check the height requirements for all the rides at both parks. At 9, she could be tall enough to ride everything, or only a few things.
If you are really worried about her not being ready yet for some of the more intense or scary rides, then I don't think going to HS instead is a bad idea. Maybe try next year for Universal. You will have a number of interesting shows, the Osbourne lights, and Fantasmic, plus a few less intense rides for her to enjoy. You could add reservations to a themed restaurant and have a great time. HS is really one of the parks that FP+ works better for if you have kids not interested in thrill rides or coasters. Plan 3 must do attractions with FP+, then spend the rest of the time watching the shows and having a nice meal, and you have successfully survived Christmas at Disney.
If you do decide to do Universal, I'd get a EP. There's no way I'd attempt Christmas without it.