Depends what you are doing. IF you are a hardcore, and I mean, HARDCORE gamer, then build your own. Otherwise, I would recomend Dell.
I built my own computer, and just a warning, it can become a major pain in the butt. I am not saying it always is, as I know some who have perfectly fine home made computers, but just as an example, my homemade PC showed symptoms of the processor overheating, only to find out that one of the hard drives had failed. That took MANY hours of work to figure out.
If you are just a casual computer user, who doesn't need the best of the best to keep up with the rest, I would get a Dell.
But if you are a gamer looking to get an advantage over your opponents, go ahead, build your own.
Now Intel or AMD... I can't really tell you off of the top of my head. I hear AMD is leading in the Computer Game market, but I do believe Intel is a more compatable processor company. I built my computer on the first wave of AMD Athlon 64+ processors and it was nearly impossible finding compatable components. Do your research, and I'm sure both are fine, but if I ever build a computer again, I am going with Intel just for the more compatability.
But if you are buying, it really just depends on the configurations.