Is it safe and stable to use titanium backup and restore at two different android versions? I want to upgrade an android phone from 2.2 to 2.3.

If I backup apps with titanium backup, will they be restored at 2.3, or will they be conflict because of different android version between backup and restore?

If it doesn't work with titanium backup, then is any other safer way?
It is usually safe to restore non-system apps and their data across different Android versions with Titanium Backup.  I wouldn't try to restore a Honeycomb-specific app on a previous OS version though, as the app itself may be incompatible due to radical changes between 3.x and earlier OS versions.

Restoring system apps and data is very unsafe.  You can introduce instabilities to your device, due to changes in the way system data is handled between major OS versions of Android.

If you are using Titanium, I assume your device is rooted, since otherwise you wouldn't be able to backup app data.  If you also have a custom recovery installed (e.g. ClockworkMod) I would highly recommend doing a full backup of the device, in case something goes wrong.