Welcome to Tom's. There are many differences, mainly in price and performance.
Please be more specific in your question. Which AMD and Intel processor line are you comparing?
In a general view, right now current AMD high end chips are on par with the last most Intel Core 2 Duo and Core 2 Quad chips (over 2.8GHz per core). Some of the highest end AMD chips can be compared with first generation i5/7 CPUs, but even the 6 core AMD cannot best Intel's latest generation of i5 and i7 CPU lines.
Another difference is that AMD chips do not currently offer integrated graphics in any of the desktop chips. Select Intel i series CPUs have an integrated graphics processor inside the CPU.
In the last few years Intel has been holding the performance crown in most all of the benchmark testing. But AMD has held the crown for pricing. You can usually pick up an AMD CPU for 20-60% less than the cost of a similar performing Intel chip.