What fundamentally separates Sonic from other characters in a 2D environment is that he's not designed to have any sort of central gimmick apart from "movement"; using Mania as an example, Tails' gameplay is all about exploration and ease of use, Knuckles is defined by his complexity and slower pacing, Mighty is about power, Ray is about aerial mobility.
Sonic's abilities in each game have generally been all about providing the player with bursts of mobility, either in the air or on the ground; super peelout, dropdash, and all three shield abilities follow this design philosophy. (Insta-shield is perhaps the sole exception to this rule.)
The super peelout, spindash, and dropdash being ground-based abilities means that Sonic, more so than any other character, interacts with the level design in a very fundamental way that has its roots in the Sonic series' emphasis on momentum and pinball physics. Sonic having comparatively less platforming options in terms of platforming compared to other characters is also compensated for by his shield abilities; this means, in addition to levels being already designed around Sonic, the shields themselves can be strategically placed in levels based on whichever would work best to Sonic's advantage.
While there are many differences between Modern and Classic, Sonic's design in games such as Unleashed and Colors similar place an emphasis on the way Sonic interacts by the level design itself through his mobility; it somewhat reflects the transition Mario made into 3D, relying less on pure momentum to gain jump height and more on a slew of mobility related tools that add a sense of technical mobility.
Without delving too much into moveset complexity, I think Sonic benefits the most from having tools that enhance the way in which Sonic interacts with the level design and capitalize on the game's core physics. I think the dropdash is a good example of this, and I think there are also some examples of modern abilities that could potentially have a use in the momentum-based format.