AMD processors are generally slower than Intel processors.
Mainly because AMD processors aren't truly advertised as much as Intel's.
Intel puts their money into advertising and researching.
AMD doesn't advertise too much which cripples their income; their fault truly.
AMD does hold a share on the graphics card market though- ATi/Radeon
And holding dedicated graphics gave them an advantage over integrated graphics.
All of that leading to the making of APU's.
APU's are processors that share a low-scale graphics set on the same die.
Intel integrated graphics don't compare what-so-ever.
AMD takes the cake on graphics.
Another thing to be aware of prices.
AMD holds to be cheaper than the Intel counter part.
AMD processors and motherboards tend to be cheaper than Intel's MOST of the time.
One thing to be sure of, Intel processors have better power due to their better architecture though.
So most of the time you really do get what you pay for.
AMD wins budget and Intel takes quality.
AMD has now looked into the RAM side of the market.
Intel hasn't a scratch on that.
AMD RAM is sponsored by Patriot; a trusted brand.
AMD wins unanimously.
Overclockability is on alot of people's mind now, too.
Almost every single AMD processor can be overclocked due to its unlocked architecture.
Intel's overclocking is locked on most processors unless you buy a "K" series.
AMD is more fruitful to overclocks.
Power and heat is a concern to keep in mind.
Most AMD processors take more power than Intel's.
Intel processors tend to get hotter though, especially the new Ivy Bridge architecture.
That is really a draw between the two.
Now onto the mobile platform of both.
AMD APU's are now being found more and more in laptops.
APU's are extremely crippled in laptops though, mainly because of the RAM.
Also, AMD APU's are clocked 1.5GHz, dual core, most of the time in laptops.
Although the APU may have a nice graphics set, the processor within can't handle it.
On Intel's side though, is the affordable mobile i3's.
For about $450, you can get a mobile i3, dual core@2.3Ghz with Intel HD 3000
That is usually enough to play World of Warcraft on good settings.
More games love Intel architecture over AMD's.
Now onto dedicated graphics between NVidia and Radeon.
NVidia cards have some quirks over Radeon cards.
NVidia has a thing called Cuda and PhysX.
Both are more for programming, 3D modeling, physics, and such. (atleast thats how I see it)
NVidia also has 3D gaming, and SLi, the combining two cards with a connector.
Radeon has the same thing as SLi but it's called Crossfire.
Radeon also has a monitors specialty, the ability to use multi-monitor setups on one card.
NVidia needs to be SLi'd to use multi-monitor sets I believe.
Radeon cards are also towards gaming, and just gaming.
A good way to see it is like this, an Xbox360 uses ATi graphics.
And the PS3 uses NVidia graphics.
Preference to the console is yours, is it not?
Drivers are a factor too.
Radeon drivers tend not to be as stable as NVidia drivers.
Simple as that.
Heat and power consumption:
Most NVidia cards use more power than Radeon cards.
And heat is a split into both, it just depends on the card.
Pricing-
NVidia cards and Radeon cards are always competing.
Most of the time, Radeon takes the cake on prices and bonuses (free games with the card etc...)
But NVidia cards are favored in more games than Radeon cards.
EX: BF3 and WoW love NVidia cards.
ATi VS NVidia is really set to your opinion on what you're looking for.
Now the verdict for a laptop.
Go with a mobile Intel processor, it handles heavier tasks.
Just keep in mind, mobile i3's and i5's are DUAL cores, and some i7's are QUAD core.
As for graphics, I don't know a whole lot on mobile graphics, but HD 3000 is enough for WoW.
Hope this all helps
Edit- I check the link to the PC you had provided.
It's nice, not a bad buy.
The difference between laptops and desktops is bigger.
Desktops can handle better graphics cards and such.
Just refer to what I said above.
Happy hunting.
And remember, fanboyism makes you an idiot.
Don't be loyal to a brand or a machine.
Side notes:
Intel's upgrade path is unbeatable with the new Z77 motherboards
Intel motherboards also tend to be nicer quality than AMD's.
Games optimize Intel/NVidia better than AMD/ATi/Radeon
Buy what you can afford.