PM said, "Questions about hardware are fine as long as it's reasonable for the asker to think it's specific to Pokémon."
This is one of those questions that I think are outside the realm of the Pokémon games themselves, even though the question is clearly mentioning HG/SS. But that's just my opinion.
On top of that it's just a ridiculous question, but one that I nonetheless set out to find the answer to.
The answer to your question is that they're all the same: 4.21 seconds.
Using L+R+Select+Start to soft reset I tested this with the DS Lite, 3DS XL, New 3DS XL, New 2DS XL, and an emulator. And aside from with an emulator, there's no faster way to reset the game/system than this.
But if you wanted to include emulation, the fastest way is to use an emulator's built-in reset button, rather than the game's. And yes, it's the same between both HG and SS.
The old 3DS hardware is identical across all three old systems (3DS/2DS/XL), and the New hardware is also identical across all 3. Therefore it's easy to conclude that it's exactly the same on those as well, since I don't have access to all 6.
DS and DSi should likewise be assumed identical if every other method, including an optimized emulator running on a PC, is completely identical to the other alternatives. I recorded the amount of time from when the screen turns white to when the music begins (the music plays just before the screen turns back on). It is exactly 4.21 seconds every single time.