Shinies always look different no matter how small the difference.
Here, Arceus shiny sprite differences were quite large.
This is a non-shiny Ghost-type Arceus.
This is a shiny one.
For Gen VI
The difference is small except in the Normal one.
This is non-shiny.
This is shiny.
However, for other forms (Grass-type as an example) here's the sprites:
This is a non-shiny Grass-type one.
This is a shiny Grass-type one.
As you can see, the skin is only slightly darker and its eyes are differently colored. That's about it.
Hope this helps!