Yes, there's so many missing details in the original post, it's difficult to offer much quality help. If it worked before and it's not working now, what changed? What are you doing different?
Go back and re-render one of the "previous movies" now and see if it plays fine on these "other devices." That would give you a clean head-to-head test with many variables the same. If it renders and plays fine, I would start thinking about what is different in the newer movies themselves. If it stutters & freezes, I'd scrutinize my output process. If the latter, simplify the file render with some alternative versions. For example, render a 720p version and test that. If you can still opt to export to Quicktime, see if you can export it as a "ProRes" file. Then run that ProRes file through Handbrake and try a variety of presets (AppleTV 2, 3, 4). Then test the various files on the "other devices."
To get better help here, share more details. Specifically:
- With what are you making these movies? iMovie? The latest version or an older version?
- What are these "other devices" (name them... model numbers too if there is more than 1 version)?
- Open up a working "previous movie" in Quicktime and "Window" (menu), "Show Inspector". Open up a problematic movie in Quicktime and do the same. Compare the information in the "Show Inspector" windows and take note of what is different. And/or screen grab each and post so that we can see those windows. You might be able to see a key difference in "Show Inspector" and it will point the way to a solution.
- Anything different about how the "previous movies" were shot vs. the problematic movies? Different camcorders? Different resolution? Etc. Again, details really help.
- Has your workflow changed? Are you importing problematic movies different than "previous movies"? Are you using different software now vs. then? Are you exporting with different options than you did then? Etc.
All such problems are usually resolved by some experiments to narrow in on specific things being done differently. However, getting help from outsiders will yield much better results if you share many more details. For example, if you share the names of the "other devices", people could confirm that Apple-generated movies stutter for them too... or play just fine. Maybe these "other devices" are just too old for newer video standards?