Hello! I'm Aidan the Hedgedog, and this is my theory! The title says it all, Mephiles the Dark is Shadow from Sonic Boom. Here is my evidance. 


In the battle, his attacks are nearly identical to Mephiles' boss battle attacks. He has Mephiles' shoot, and his charge. When he charges, Shadow turns red, much like Mephiles turns purple when he charges. Also, in the battle, you and Shadez travel thru time, much like how the BBs against Mephiles take place in different times. Also, he states that friendship is weak, and, Mephiles hates friendship.


His chest hair is exactly the same as Shadow's, and so is his fur.  Also, you can tell by Mephiles' muzzle he is smirking most of the time, just like Shadow. Also, both of their spines/hair are sticking a curved way up, and have the stripes inside their eyes, instead of outside their eyes. And as a matter of fact, their bodies are bent at the waist in most poses. (See the pictures at the right side.) Also, by recoloring Shadow, I learned that it's just a modified version of Mephiles. They also wear the same gloves, with the same differences as eachother against Normal Shadow's.
Mephiles 3

Voice and other small changes/simalities/etc.

In Sonic Toon, Shadow has a very deep, scratchy voice, much like Mephiles'. They have the same motives, but with different scenarios: To kill/defeat Sonic to stop/destroy sometime in the future. Also, Mephiles says that Shadow will end-up like him, which may hint that one day Shadow will be him. Shadow did give Mephiles his new cooler looking form, and the visor that Lyric controls him with is Purple, like Mephiles' chaos emerald. This may mean that Lyric wanted to control Mephiles, so he found the Purple Emerald and used it's power to make the visor. Also, in Sonic 06, Mephiles indirectly claims multiple times he is Shadow's superior, and Shadow quotes: I go alone. I'm leaving, as your superior. Also, their skin tones have very minor differences, like Mephiles' being a bit more paler then Shadow's. Also, Shadow's origanal name was "Terois" which means "reflectoin of", and what is Mephiles? Shadow's reflectoin. Also, Mephiles' name is from Mephilestophiles (I hope I didn't bucter it), and The Devil (did'nt wanna have to rewrite it) always took the form of a shadow. Also, Mephiles takes pride in the suffering of others', and Shadow takes pride in crippiling Sonic's ego, which are the same type of social crime.

Welp, that's my theroy! Hope you like it, and tell me what ya thought!