Probably not as many as you might assume. There's also the issue of the Game Boy running on an 8080 derivative, unlike the NES and Super NES, which ran on 6502 (and 65816) derivatives.

You might be interested in these articles covering each console's architecture:

* NES https://www.copetti.org/writings/consoles/nes/

* SNES https://www.copetti.org/writings/consoles/super-nintendo/

* Game Boy https://www.copetti.org/writings/consoles/game-boy/

Former SNES and GBA hobbyist developer here. The different CPUs aside - Z80 in the GB, 6502 in the NES, 65816 in the SNES and ARM in the GBA - the GB, just like the NES, shares very little with the SNES. The GBA is a different story: it is in so many ways like the SNES' sibling, but an improved sibling, most distinctly because of its open memory architecture allowing convenient and fast access to all of its custom hardware, whereas in the SNES the video and sound chip RAM is tucked away behind single-byte-sized memory channels you have to access by shoveling bytes manually (or by programmable DMA) back and forth between CPU-accessible RAM and video/sound chip RAM etc. This architectural choice was in my opinion the largest improvement the GBA brought, more so than moving away from the SNES' custom "sound computer" which was a bit of a hurdle.

Now that you mention the sound, I always had this question: was the GBA sound system any good? My understanding is that the GBA only has the original GB sound chip plus two PCM channels, without any dedicated hardware synthesis or mixing, so all sound effects need to run on software. Now the CPU was so much faster than the SNES or Megadrive, but was it fast enough to make up for it?

GBA games were generally regarded as having lower sound quality than SNES games, although this perception was somewhat exaggerated by the poor quality of some SNES->GBA ports. It took a lot more CPU to get good audio out of the GBA, and I'm sure developers were taking the GBA's tinny speaker into account when deciding how much effort to invest in polishing the soundtrack. Hell, the GBA SP needed an adapter to use headphones!

It has the GB legacy sound and two 8-bit PCM channels (stereo wave output basically). It is definitely worse than the SNES - however, because of how fast the ARM is (relatively speaking) it has no problem doing software mixing to provide developers with effectively 4, 6 and even 8 channels of PCM audio for soundtracks and effects. Not as smooth sound, but totally sufficient.

The Game Boy is much more similar to the Sega Master System & Game Gear than to the NES. Some games (e.g. Lemmings 2, Pinball Dreams, Spirou) were developed for both handhelds (or even for all 3 platforms) using a single assembly-language codebase.

The GameBoy is distinctly different from the (S)NES. It uses an 8080/Z80-ish CPU core instead of the 6502/65816, the audio and graphics hardware have different capabilities than the NES, etc. There were a lot of games that were both on the NES and the GB but they were rarely 1:1 ports for these and other reasons.

They're basically completely different other than broad architectural strokes. Different CPU ISA, the keys are sampled through a matrix rather than a bit banged shift register setup, audio channels are pretty different, GPU is internally pretty different (LCD allows pauses in the pixel stream unlike a CRT so the GPU uses that), etc.

The Super GameBoy comes to mind. Was it a full-fledged emulator or did it use any neat tricks to run GB code directly on the SNES?

It wasn't even an emulator, it was a complete gameboy SoC with the pixel stream routed to the SNES's VRAM rather than an LCD screen.

The Super GameBoy is essentially full GameBoy hardware in a cart, that hijacks the SNES PPU for video output and uses SNES controllers for input. There is no hardware emulation going on.