Both of the fusions we've seen of Garnet (not including Ruby and Sapphire) have had some sort of special visualization. Sugilite had some sort of dragon breathing fire, and (Spoilers) had a (Spoiler) visualization. We haven't seen Alexandrite's actual fusion, but I assume its the same way. All of the other fusions are just basic light-form melding. I think that any fusion involving more than 2 Gems get these kinds of special visuals, although for what reason, I'm not sure.
On a related note, both of the fusions we've seen with Pearl show that her dances are more involving of the other partner. When Garnet and Amethyst formed Sugilite, they were dancing on their own until the finale, whereas to form Opal and Sardonyx, Pearl actively went to her partner to continue the dance.