Got carried away and decided to test every DS game....
HG/SS load the same on every system. Other Pokémon games vary.
Platinum seems to vary by 0.05s regardless of the system.
Pearl is 3.333s on every system
Black and Black 2 are faster on a DS Lite.
I think this is because Gen 5 is DSi-enhanced. It must take longer for the DSi systems to load(?)
The fastest way to reset HG/SS (or any Pokémon game) is the built-in L+R+Start+Select method.
I decided to test this again to provide video evidence. In doing so, I realized that I timed it incorrectly the first time. Sorry! I was counting the frames of the video, not the actual elapsed time. I noticed this because when I used a different camera the number went from 4.21 to 4.25. I can’t believe I didn’t realize this before, especially when the playhead is clearly closer to the 5 second counter. The real number appears to be about 4.958. Well, technically that’s when the screen begins fading back in. The full cut always occurs at 5 seconds exactly. Nearly a second slower than my initial claim, although the answer to the question remains the same. The Nintendo 3DS uses an ARM9 processor to boot into DS mode to run the game. The hardware it accesses is identical (I think?) to the cpu in the DSi, which is twice as fast as the original chip in the DS/Lite. You’d think this would speed up the launch of the game, but it apparently doesn’t (or isn’t allowed to). However, emulators boot significantly quicker. The fastest emulator I tested on, believe it or not, was the Wii U’s proprietary DS emulator. Good job, Nintendo!
In every single test, the 3DS and N2DS reset in 4.958 seconds. The DS Lite matched this time except for one outlier which lasted 5.125 seconds. Every other test was 4.95 so I’m not sure what happened there.
My number is only as accurate as my camera’s framerate. More frames means more accurate millisecond counting. I’m sure you could get way more accurate than 4.9 seconds. The actual value lies somewhere between 4.91 and 5.0. And maybe if you had an insanely accurate method, you could prove that there’s a slight variation between soft resets.
But the point is that when you record them and put them side by side, they match up perfectly:

By the way, sometimes the game fades to white/black and sometimes it’s an instant cut. It happens on every system so it appears to either be a quirk in the game or a limitation of my camera’s framerate. In the image above, it might look like the DS Lite is slower because the two images on the left begin fading-in one frame faster. I do not think it affects the actual timing of the reset. The full cuts always happen at the 5 second mark (5.0). I think my phone camera just doesn’t capture the fade perfectly every time.
The audio also loads in slightly different each time. Sometimes it’s faster, sometimes it’s slower. In my original tests I claimed the sound played before the video fades in but that didn’t happen this time.
Also I’m sorry for calling the question ridiculous before I didn’t mean to belittle you but I can see how it may have come across that way.
I am interested in silly stuff like this anyway and I learn things along the way so it’s ok that I spent a whole day staring at a SoulSilver intro screen.
Platinum
Pearl
Black
Black 2
SS