From a few years further down the road I will say that in our case things did get better, but there are still some struggles. Where possible we let them lead the way and they tackled what we and they thought they could handle. We tried to make sure that we had an easy out if either one got overwhelmed. We paused movies and went back to them. We would cover eyes and ears through the parts that bothered them and then uncover when everything was OK. We pre-srceened nearly everything when we could but that gets more difficult over time.
Both my kids (DD11 and DS9) were like this. In addition to the emotional aspects of the story, DD11 was utterly overwhelmed by the whole theater experience. Going to see Frozen a few weeks ago was the first time I've seen her really enjoy a movie in the theater. We don't even attempt 3D.
I remember having to take her out a daycare situation at about 3 years old. They had the kids watching Disney movies in the morning while eating breakfast. I usually dropped her off before the TV was turned on so didn't realize what was happening. One day I had to run home for something and came back to find my DD(then 3) sitting at the table bawling her eyes out, while a Disney movie was on the DVD player. She was scared by the characters and the story but the teachers simply couldn't understand why she was so upset - all the other kids were fine! I pulled her out then and there. Both of my kids still climb into my lap and cover their eyes during the scary or overwhelming parts of movies we watch at home.
For DD11 it even applies to some reading. She put HP Book 5 down with about 30-50 pages to go (I think about when an important character died) - finally picked it back up a week or two later and finished it, but then had no interest in the remaining books for almost 2 years. Finally read both this past summer.
The demands of school are creeping in. Previous years we got permission from teachers for her to leave the room during oral reading of parts of books like Stone Fox and Land Remembered, because she found them overwhelming. That requires knowing ahead of time what the lesson plans are, because most teachers don't see a problem.
Now I can't seem to plan ahead, so we deal with the fallout after the fact. They read Poe last year in class and she had nightmares for a week. She attended a play presentation this year as part of her Language Arts class (7th grade) which included several Poe short stories as well as "The Monkey's Paw". Although she made it through the performance, the nightmares were back for several days and she could not remotely cope with the homework assignment to summarize and describe the plays, so we skipped it.
The conflict themes in higher grade level reading requirements are becoming a problem. She recently had to do a book report that was required to be at least a 7.5 grade reading level. Finding a book at that reading level with a manageble level and type of conflict was something of a challenge. Finally settled on The Incredible Journey after I promised her that none of the main characters died (and she remembered having seen the recent Disney version of the movie Homeward Bound).
Letting the kids lead and have control over what they watch and read has been our biggest success. Having them know there is no pressure and they can bail at any time and come back or not gives them control. Pre-screeing and being able to provide assurance of at least the general outcome (while leaving out as many details as possible) lets them trust you and the movie that 'everyting will be OK'. I do have to say that we may have taken this part a little too far as DD11 is now quite cynical about the 'happy ending' in nearly all age-appropriate movies. The 'have to do it' stuff for school is quite another story and has only served to reinforce my belief that letting the kids figure it out at their own pace is what works best.
DS9 has pretty much grown out of it - he is still quite sensitive, but seems to process it differently. I think the boy peer pressure thing is starting to kick in, because the response at school or in public can be very different from the one at home.
Good luck!
