The GBC is to the GB, what the DSi was to the DS and the N3DS was to the 3DS. Both in a figurative sense and in a literal sense (all three systems saw almost exactly the same hardware bump; double the RAM and CPU power, along with at least one unique hardware gimmick each).
The GBC is a hardware revision of the original GB and is not a unique console in its own right. Don't let anyone convince you otherwise.
People are dumb though and discount exclusive downloadable games, pretending that they don't exist; as if they're not real games, so they don't realise that the exclusive libraries of each system are actually very comparable in terms of size. Also GBC was first, so people like to pretend that it was somehow different.
This is a real pet peeve of mine in case you couldn't tell!
Disagree. When GBC was released Nintendo treated it as a complete replacement: all previous Gameboy console distribution was immediately stopped (in the US at least), unlike DSi and n3DS. And GBC was clearly more powerful even than an NES, with more internal features than just "faster CPU/more memory" and that power let developers push the system *way* beyond what old Gameboy could do (example, game cartridges could be twice the size of old Gameboy games). And after a few months developers stopped making games without color support, and started transitioning towards GBC-exclusive games, to a point where no old Gameboy-compatible games were made anymore, something that didn't happen for DSi or n3DS. Also, Nintendo put a HUGE advertising campaign behind it, much more than DSi and New 3DS (DSi Nintendo even tried to hide the extra power from consumers, only talking up the camera, digital store and form factor).
And sure, those DSi eShop games were "exclusive", only because of the distribution method; only a small percentage took advantage of the DSi's extra capabilities. And many were small games that would never have been sold as separate exclusive cartridge games, unlike the GBC's exclusive games.
And of course, going from 4 shades of grey per screen to 52 colors per screen is as big a jump as 2D to 3D, especially when developers could use tricks to increase that to thousands of colors per screen.