I try sometimes when i'm bored to catch shinies and i just do not seem to have the right technique...
They are basically the same thing in terms of Chance. But I would say a Shiny Legendary is easier due to the fact that you can Soft-Reset in front of the Legendary until it is Shiny, and not find it randomly. But this is based on opinion, so what does mine matter? ;)
Info on Soft-Reseting.
There isn't a difference in chance.
Shiny random pokemon cause usually on special events you might get shiny legend when you dont get a shiny random pokemon.