Memento's firmware that allows you to use the PS2 Memor32 USB memory card to play PS2 games shows that it can boot a back up PS2 game quicker than the original by a few seconds! The first video compares the boot up speed of an original Gran Turismo 3 (GT3) to a back up copy on a unmodded PS2 in just 16 seconds and 11 seconds, respectively. The second video shows The Bouncer's boot up speed at 22 seconds for both original and back up.
You can purchase the Memor32 from Divineo Germany, Divineo France, Divineo Spain, Divineo Italy, Futura Videogames, MrModchips and ConsoleSource.
GT3
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Source: YouTube