Man, when I think about what 'Sonic', Shadow, and Silver share, the first thing that clicks for me is the way they all tap into big, flashy energy systems — the Chaos Emeralds being the obvious common thread. In games like 'Sonic Adventure 2' and 'Sonic Generations' I loved watching each of them flip into a 'super' state using those gems: Super Sonic, Super Shadow, Super Silver. That transformation gives all three flight, crazy durability, and a huge boost to whatever their main thing is (speed for Sonic and Shadow, psychokinetic power for Silver).
Beyond the Super forms, they also share a broader set of overlapping mechanics: energy projection/manipulation (whether it’s Chaos energy or psychic constructs), temporary invulnerability when powered up, and a tendency to warp space or pause time in fight scenes. Shadow uses Chaos Control to teleport or slow time, and Silver bends the environment with psychokinesis — Sonic has used Chaos Control too in certain titles, so spatial tricks are something they can all pull off under the right conditions.
On a softer level, I also see a shared theme of willpower and internal strength. They’re each written as characters who push reality around them when they absolutely must, which is why their abilities often feel like different flavors of the same cosmic toolbox. If you’re trying to mash them together in a fanfic or a game mod, lean on those shared tools: emerald-powered transformations, energy manipulation, and space/time tricks — they’ll make the trio feel naturally cohesive to fans.