for Debian based distros, I would normally recommend a clean install after a proper backup is done.

That's actually a very good way: no risk loosing anything and at the same time preserve a clean environment. Of course it takes some additional time.

Another safe way is to run aptitude, upgrade the list of packages (press U) and then try to do small upgrades step by step, checking each time that there are no conflicts. In case there are some, explore the suggested possible solutions and choose the one that represent the best fit for your needs.

As for TDE 3.5.13.2 --> TDE 14.0.0 upgrade, a lot of packages have been renamed, in particular kdelibs4c2a has become tdelibs14. That means that the upgrade will have to be done as a single step. Expect several packages to be removed and do not forget to manually select the new renamed packages to be installed if needed (ex: kdebase is now called tdebase). Overall, I would suggest a backup and clean installed, as Michael already said.

Cheers Michele