When is an Archon better than two Dark Templars?

Archons are good against air and ground and do splash damage. If your opponent has countered your cloaked units with a detector unit then I would merge. I almost never use dark templars over High Templars because I think High Templars are a lot more useful and versatile.

One time would be when they have sufficient detection but you are able to save your Dark Templar somehow, either escaping them in time or seeing the detection in advance. Dark Templar are not effective when the enemy sees them coming (or sees them at all), so it is generally better to have an Archon than 2 visible Dark Templar.