It's not that simple. The GBA uses an ARM7 and the GP2x uses an ARM9, first of all-- they are from the same architecture but not the same generation and are far from identical designs. Secondly, you cannot natively run code like that even on the same architecture as it would require 100% direct hardware-level access, as in "No OS" in all likelihood, to function-- there would need to be a working interpeter to translate the ARM7 code to something the ARM9 will understand, and there may be instructions in use that don't even exist on the ARM9.
Additionally, the GBA is NOT just an ARM7-- it also has a custom 2D processor that handles all graphical work, as well as niceties like hardware-accelerated scaling and rotation.
Simply put, you can't just drag-and-drop an ARM7 program onto an ARM9 system and expect it to run at 100% just like that. Also note, GBA emulation is very slow on the PC side of things as well-- the system is much newer than the PSX-- there are nowhere near as many emulators for it, the science of emulating the system is far from perfect. Very far.
In short, have patience.