In addition to what tehbeard mentioned, Xemu at least (which is what i have experience with as i used it to do some homebrew development[0] with the open source nxdk[1] SDK) is far from accurate and largely just a means for playing OG Xbox games on modern hardware. However the GPU emulation does not take into account NV2A's performance at all and simply translates the calls to OpenGL (despite the "DirectXbox" name, the GPU is actually designed around OpenGL :-P) so it is much faster than the real one and depending on what is going on the CPU performance can also be quite faster. IIRC it doesn't even emulate the real CPU the OG Xbox has as you can accidentally use instructions in Xemu not available on the real hardware.

Of course if your goal is to just have games from OG Xbox playable on a PC that is fine (if anything for most games it is an improvement as they'd run smoother) but if you want cycle accurate emulation it doesn't fit the bill. In that case basing the emulator on something like 86box might be better as that has been designed with the goal of achieving cycle accurate PC hardware emulation.

[0] https://www.youtube.com/watch?v=gQpK6eX-04M

[1] https://github.com/XboxDev/nxdk/

The key part there is that the original xbox is a Pentium III PC with, iirc some northbridge/southbridge shenanigans.

And the PS4 uses a custom AMD x86-64 chip.

An Xbox 360 is slightly more difficult as that is a PowerPC architecture (RISC vs. CISC of x86) Same for the PS3 except you also have those incredibly weird "SPE" cores to try and emulate as well.