It is canon that synthetic crystals produce more powerful lightsabers.
It's written in The essential guide to the Force.
According to this source, more powerful means:
- more cutting power
- possibility that a natural crystal lightsaber will be short-fused in a duel
- it's harder to move due to a stronger gyroscopic effect.
Additionally, according to the wiki page,
A standard synthetic crystal was created through the successful replication of the geological structure of natural crystals. Standard crystals set the baseline for synthetic crystals in general; they generated a more powerful lightsaber blade than natural crystals, and often demonstrated a red coloration, though that was easily controlled. In fact, synth-crystal blades were so powerful that they had the rare potential to "break the blade" of standard lightsabers by overloading the energy matrix and instantly burning out the other lightsaber. Though this happened extremely rarely, it was a known and frightening possibility in combat.
However, synth-crystal generated lightsaber blades were in general less maneuverable than the blades generated by natural crystals, and were generally more unstable.
EDIT: It happened once:
I'm quoting from Jedi Master Pernicar, C.1010 B.B.Y. , in The Essential guide to the Force page 109.
Indeed, this is rare, as I have only once seen a Sith lightsaber "break" a Jedi lightsaber on one occasion, something I believed, at the time, was a defect in the Jedi weapon.