Going with an AMD chip can save you some money since they don't spend as much on advertising and the like, so their cost is usually less than a comparable intel chip. As far as how they work, cpu are nothing but a bunch of logic gates. The only difference is their architecture and the clock speeds they run at. Remember faster speeds do not always mean more performance. As far as Dell, their stuff is fine. Just make sure you get a warranty if you are getting a laptop, they are fragile little suckers.
Just an interesting thing I heard once: The performance and budget intel lines are identical, except that the budget lines have some of the cache damaged to decrease performance. Its more cost effective for them to make all the chips identical.