Here are some very simple things that are different between them:
For gaming systems it is more a question of taste and money than a real difference. Both platforms have their advantages:
Another user said:
Intel processors have a more diverse library of CPUs than AMD, and have higher-end models too, they also have "hyperthreading" which theoretically doubles the amount of cores in your CPU.
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The AMD Processor is slightly cheaper, however its single core performance is slightly less good than Intel's. AMD also consumes a bit more power than the Intel processors.