Hello! The advantages from running on Xbox as opposed to 360 come from the game being installed onto the hard drive. The first one is faster and more consistent load times. I used to have randomly longer load times on 360 for no reason, but switching to OG Xbox fixed the inconsistency. The other is less reliance on 360 emulation which is prone to random crashing and increased chances of crashing at certain points such as entering Knothole Glade and Prison Path (Mytus and I have both crashed in those places more times than we would like to talk about lol).
The absolute slowest way to play is with a game disc on either console. Having the game on a 360 HDD cuts loads basically in half, 360 SSD shaves a couple of seconds off loads from that, a stock OG Xbox's 5400RPM IDE HDD was tested as a few seconds faster than that, and then 7200RPM IDE and SATA drives tested to be roughly half a second faster than that, and there was no real benefit from having an OG Xbox with an SSD due to the architecture being a bottleneck for an SSD's speeds.
That said, if you only have access to one, I'd say to stick with that to get your foot in the door for running, but definitely try to have the game installed on your console's storage drive if you can do that. :)
