Just out of curiosity, I tested this myself (old 3DS + cart) without SD card and no internet to skip the update message, and using the power button method was actually one second slower than quitting via home menu. It might be faster on a n3DS though.
I'm kinda wondering if you can save time by getting rid of the streetpass stuff somehow via custom firmware or something :/
I tested on a N3DS Digital copy, and I'm pretty sure internet was off. Don't really know my SD card specs, though.