Probably a lot more than the ARM11..
I don't really see a reason for hardware much more powerful than an ARM9 around 300 Mhz for gaming applications, though.
Let's take for example, the originally-planned specs for the XGP. The 2D/3D accelerator in the originally-selected MagicEyes VRender-3D chipset (believed to be the same one used in Samsung's S3C2460) ... it is able to render 1.0-1.5 Million polygons per second, and has comparable 2D capability. This places the graphical capabilities of a handheld using it several notches above the N64's graphical capabilities (most games did not utilize greater than 30% of the N64 GPU's capability for price-related reasons.) Its 200 MHz ARM9 processor, running integer-only or fixed-point code, is roughly on par with the Dreamcast SH-4 processor's integer capability. The comparatively immense quantity of RAM available (very fast RAM at that, MobileDDR) and support for very large games given maximum SD card size make it very clear that homebrew games have the potential to soar far and beyond anything available on the GP2X or GP32-- treated not like just a homebrew platform for emulation, but a console in its own right, such a machine would be a truly incredible gaming platform. The mistake that is maken all too often is relegating the GP2X's capabilities to be that of the systems it emulates-- which isn't fair in any sense given the enormous overhead emulation carries.
This is not to even mention the possibilities with the more powerful S3C2460. A 66 MHz faster processor, bringing it up to 266 MHz. A full floating point processor that is as powerful as the main one, and can perform vector processing-- not only will floating-point heavy code run at full speed, but it will run FASTER than an integer/fixed-point only program. A 16-bit DSP at 100 MHz will provide even more processing capability to developers who how know to effectively utilize it-- and due to the superior internal architecture compared to the GP2X's MMSP2's layout, it should be much easer to utilize than the ARM940T, due to lack of the memory contention, cache and bus accessibility issues that plague the 940T. Other improvements are that SD Direct Memory Access (DMA) should be fully functional (it is broken in the MMSP2, causing the CPU to stall whenever the SD card is read from, or written to) allowing realtime loading/saving of data without slowing the rest of the system; as well as that the hardware JPEG decoding support would allow large 3D textures to be decompressed into memory far faster than is possible with purely software decoding.
When you look at CPU performance rivalling high-end consoles and PDAs, 3D capabilities exceeding the N64 and probably matching those of the PSP, 2D capabilities to an absurd degree, and an incredible about of RAM and game storage space available, it's hard to see why anything beefier and more expensive is necessary-- a system with either of these SoCs, epsecially the S3C2460, would be an incredible platform for any developer or user, and possibly the greatest gift to the open-source gaming community since Linux...