*sighs*
I see both sides going about this the wrong way.
While Shadow being a Sonic semiclone would make a lot of sense, just giving minor changes to some moves is not the route to take it.
For example, we have Sonic's Neutral Special, the Homing Attack.
Shadow has been able to perform this since his debut. However, Sonic 06 introduced a special variation of this: Chaos Attack.
With this, Shadow would start off similar to Sonic and rise in the air, then home in on the opponent as he hits the opponent, the player can rapidly press either the attack button or special button (whichever works better for this) to rapidly assault the opponent with punches and kicks.
Now, Shadow needs to Spin Dash. It's iconic to nearly all major Sonic characters, including him.
What I propose as an idea, is that Shadow takes Sonic's old Side Special version of it, leaving Sonic with just the Spin Charge Down Special version. Why? For two reasons:
1. Sonic's Side Special represents how Spin Dash works in Modern titles, while Sonic's Down Specal represents how it works in Classic titles. Shadow, being a Modern character in his debut, would sensibly use the Side Special version.
2. Sonic Boost has become a major part of Sonic's gameplay since after his Brawl appearance, much like the Homing Attack did after Sonic Adventure. Sonic using the Sonic Boost for a Side Special to replace his older one is beleivable.
Springs, don't use them. Sonic only uses a Spring because there's not much else he can do for a recovery.
Shadow has his Chaos Abilities, including a teleportation.
Since two Spin Dashes would be redundant (like in Brawl), this move is open to anything, really. My personal preference would be the Chaos Spear, yet another iconic ability for Shadow. It could theoretically be like when controlling Super Shadow in his own game, press the special button rapidly after firing to rapidly shoot smaller, weaker bolts, or hold the special button after initiating the attack to charge a larger, stronger bolt.
Final Smash, I had an idea where Shadow would briefly turn into Super Shadow, unleash the Arrows of Light ability Super Shadow had in Sonic 06, then revert to normal.
EDIT: Then we get into normal attacks. Those would be as different as Ness and Lucas, considering Sonic has his style of fighting and Shadow has his. They contrast.