Look up Lenovo y510p. The cheapest one usually sits right around $800 and is a pretty good system
Or the y410p is pretty similar to it but cheaper, though it has a smaller screen, and doesn't have a number pad on the side.
As for in general while looking at other specs, Intel has much better CPUs than AMD. AMD's CPUs are only really considerable if you are looking at cheap laptops below the Intel i5 price range. On the desktop market I think AMD is pretty good price/performance wise, but its the same scenario there really. The best AMD desktop processor fights with the lower Intel i5's.
For graphics Intel is on the opposite side of things with much weaker graphics that only compete with the lowest end chips from AMD and Nvidia. Here is a quick naming guide to help.
Nvidia:
###X. Example: 620M
The first number, in the example "6" is the series of cards.
Second and third numbers are the card rank in the series, in the example "20".
The "X" is just a letter. In desktop cards there isn't a letter, and on mobile cards there is an "M".
The higher the first number, the newer the technology. Its more recent. The higher the 2nd and 3rd numbers the better the card is in that series. They usually go up or down in increments of "10" but on the mobile ones its not too uncommon to see them go by increments of "5".
AMD's old naming scheme is pretty much the same. For example "7850". Drop the "0" at the end and its the exact same as above except that 3rd number can be either a "3", a "5", or a "7" but its never anything else.
The new naming scheme for AMD is a bit different and I am not the best person to describe it to you.
For Intel's graphics, they are really low end. There best mobile graphics "Intel HD 4400" is only a little better than the "Nvidia GT 610M". The "Intel HD 4200" is pretty much the same, and the "Intel HD 4000" is just a little weaker being a tie to the Nvidia GT 610M.
As for which is better overall, neither AMD or Nvidia is really better than the other, so it all depends on which specific cards.