You can actually see that they stack (by clicking on details or the stat button when looking at a hero in the equipment or hero sections of the main screen)). The stats shown include the set bonuses. If you take set pieces off, you can watch the stats drop.
As Trisen said, the priest’s holy armor is definitely worth having 5 of the set.
The mages are stronger with partial bonuses from 2 different sets (of the same star level). I also aim for that. A possible exception is the 4-star 5-piece set that allows your fireball to hit up to 3 targets. I found it very handy, for a time, to use that set on my strongest overpowered 6-star mage in story mode. It’s far better to barely kill 3 monsters than obliterate 2 monsters off the face of the planet. It only works if your mage is overpowered though. Not recommended for weak mages. Barely wounding 3 monsters isn’t all that helpful.
As for the guardian armor set, it depends. I’m using the 5-piece set for the 40% HP bonus. One of my pets heals based on HP, so that bonus helps a lot.