Backup app data and restore across ROMs I always use Titanium Backup to backup my apps' data.

However, last time I tried switching to a different ROM, it didn't
work very well.
I let the apps be installed automatically by android, and then tried
restoring their data with TB (user apps only, no system apps), but
this caused most of my apps to always force-close when launched.

I was forced to switch back to the previous ROM to be able to get my
data back.

So I ask: is there an app (other than TB) that's more stable when it
comes to restoring data backed up in a different ROM?

Again, I'm talking about user apps, I know it's unstable to restore
system apps and I don't need that.
Restoring across different ROMs, have you considered the "troubleshooting options" of TB, and e.g. enabled its migration mode, or have it using the system's own SQLite libs instead of TiBus? All those things are especially for cases as described with your question. So making use of those might end your search for an alternative; they've always worked for me – migrating from my HTC Wildfire via Motorola Milestone 2 to finally LG Optimus 4X.

If you insist on alternatives, however, I'd suggest you take a look at the backup tag-wiki, where you find many of them described. With Android 4+, you could e.g. make use of adb backup (or use Helium Backup on your device, which does the same locally). Again: This and more is described in the mentioned tag-wiki.