I'm 15 years old and have been to both Universal Studios (and IOA) and Disney.
I haven't been to Animal Kingdom at Disney, so my post for Disney vs. Universal is mostly based on Magic Kingdom where I visited the most.
Disney just has what I feel a youthful environment. Some place kids 10 and under dream about going. Most rides aren't very exciting with exception to Splash and Space Mountain (but those are almost inadequete (sp?) compared to Universal).
I went to Universal for my first time (well, not counting the time when I was 3 when I couldn't really have any opinion of the place) in 5th grade and thought it was ok. Some of the rides scared me.
I went back when I was 13 or 14 and liked Universal a lot more. I liked Islands of Adventure better (gotta love those rollercoasters...which unlike the ones at Disney actually go upside down!). I liked Spiderman, Hulk, Popeyes water ride, and Jurassic Park River Adventure.
This year, I can not emphasize enough how much I love Universal. Better than Islands of Adventure, even! But, tastes change. I love both. I liked the shows at Universal a lot. Especially Ghostbusters and Horror Makeup Show. I liked the rides based on movies I've seen like Men in Black, Back to the Future, etc. And since I'm *so* interestyed in film, seeing how they make movies (like the preshow for Earthquake ride) was very interesting.
Basically, Universal Studios is the more "grown-up" theme park. With exception to ET and Jimmy Neutron of course. Especially with the shows there may be some things said that would NEVER be said at Disney (sexual jokes). Many will fly over your 12-year old's head and they are well done (not overdone where it's not funny).
But don't let that scare you!! All shows are well done and BOTH daughters will probably LOVE Ghostbusters show!! My mom and I love it (seen it over 30 times...lol). That one is "clean".
Rides are better than Disneys. Shows are better.
I don't know who had bad experiences with the staff but I've ALWAYS found the staff at both parks VERY friendly everytime I've went and so far I've been around 20 times).
Your daughters may like a more grown-up park because most everything is less "cheesy" if you get my drift.
I could go on everything at Disney when I was 8 or 9 years old. I'm older now and I like Universal better. Give it a chance and maybe you guys will have fun. I always do! I'm even asking for the annual pass for the 3rd year in a row for next year!!!!
Hope this helps
Sorry it was so long!!