Very simplified answer
The full story's pretty involved and would be too much to fit into a short answer on StackExchange. Below, most of the statements are simplified, and shouldn't be taken as technically correct so much as to give a gist.
I use to access the internet with an AMD Phenom II with 6 cores and I could almost have as much tabs open and almost everything is instantaneous. Then for the past 3 or so years, I've been accessing the internet with laptops and netbooks, which were Intel Celerons and Atoms and i just isn't like before.
Celeron's are cheap, low-end CPU's. Computers that contain them will generally be built from cheap, low-end parts. Atom's are meant to be small, portable, and low-power.
Neither will give you performance desktop results. That's not what they're for.
Supposing AMD Phenoms are comparable with Intel Cores (i3, i5 or i7s)
They're not. As far as I can find, they stopped making Phenom's quite a while ago, so they're old processors. AMD chips from 10 years ago aren't comparable to modern Intel i7's.
AMD Phenom's and Intel Core's use the same basic CPU architecture, x86-64, so we're able to compare them based on their metrics with some reasonable accuracy.
Variations in chip features (e.g. cache, pipelining, branch prediction) will cause further variation. Recently, Intel's been doing better than AMD with regards to this stuff, so Intel chips will tend to do better than comparable AMD chips with this sorta thing. Usually AMD helps to make up for this by offering more cores in their CPU's, which is great for other stuff, but irrelevant here.
I've always assumed them as high performance threading (Hyper-threading in the case of Intel) and multi-coring.
I've thought of branch prediction for a while, but I know that most of AMD's architectures aren't as aggressive in branch prediction compared to Intels.
Yup, that's a minor factor in Intel's favor. But, you can mostly ignore it for now since it's probably not as large as other factors.
But does SIMD (MMX, eMMX, etc) performance also count?
Does GPU performance matter?