My computer would not turn on

For some reason this old crappy computer (like 5 years) I have would not turn on today. It had done the same thing a few months ago and I had fixed it then but now I just don't have the time to mess around with it so I took out the parts I need and SMASHED the crap out of it. Then I went to Best Buy and bought a Gateway GT5220 (maybe for temporary use). Here are the specs on it

liProcessor AMD Athlon™ 64 X2 Processor 3800+
Dual-core 64-bit processor with AMD64 Technology
(2.0GHz, 2000MHz FSB, 2 x 512KB L2 cache)
liDual channel 1GB RAM
liNVIDIA® GeForce® 6150LE (Crush51)

The question I have is how is AMD different from Intel? Is intel's core duo better than AMDs? The price was way cheaper than the Intel ones and I thought may be there is some kind of weakness in AMD. I am not a computer gamer so I am only going to use it to watch movies and do normal stuff on it. So far I like it way better than my old one. It runs really quite and runs pretty smoothly. I put in my old graphics card instead of using the built in one. What do you guys think? Is it a keeper?

Thanks,
Ti