Well any machine can emulate any other machine regardless its cpu, memory, gpu, and etc.. It comes down to the emulator fast enough to be usable. I have written NES and SNES emulator myself. I know it's no big deal, but enough to know how emulator works.
Like WOWchamp said, the system has to be 10x more powerful to emulate other machine in software mode. It is all about the raw power of CPU. It has to emulate the opcodes of CPU, GPU, how the data flow between them, how do they fetch data from the memory and other stuffs. Plus you need to have enough memory and/or hard drive space to allocation space for the main memory, sound buffer, and vram.
Let's said Xbox has P3 733Mhz CPU, NVIDIA graphics processor and 64 MB of RAM. You need a roughly 7Ghz CPU and around 512Mb Ram just to emulate those. Even the multi-core CPU only can help very little.
So Xbox or Xbox 360 emulator are possible, but totally unusable. You might looking at max of 1 frame per every 2 to 3 seconds.