Well, they both execute the same x86 instructions (well, they may not always support the same extensions like some SSE, AVX, etc.), so they can both run Windows or whatever applications you want and output the same data. However, there are significant differences in architecture--the design of the circuit--that influence how quickly they get the job done running different types of computer code. These differences and why they impact performance are probably subjects with too large a scope for a forum post. There are also significant architectural differences between different generations and types of AMD processors as well as between different Intel processors.
The pricing mostly reflects differences in performance, but with many exceptions. At the moment, at least before AMD's next-gen Bulldozer is released, AMD CPUs are slower at most jobs than recent Intel CPUs. These are some terrible overgeneralizations though, but maybe you'd get a more precise answer if you asked a more specific question.