Im going to be buying a new laptop before Christmas and do not know what processor I should be looking to buy. What are the advantages/disadvantages of the Intel vs AMD processors and within each company what kind of performance differences can be seen from one processor to the next.

The Core 2 Duo is the undisputed king of mobil CPU's right now, but you have to watch out which "model" you get. It isn't as easy as just Core 2 Duo.

The AMD X2 Turion dual core is not a bad CPU, and with the new AM2 platform MAY be upgradable to the next gen of chips the 4x4 Quad Core which AMD should regain the upper hand.

The X2 runs a little hotter, and uses more juice than its Intel counterpart.
Many times it is hard to find an X2 with a decent GPU in it, that is one MAJOR drawback AMD has. An nVidia 7600 or x1600 is probably the best you are going to do right now, maybe an x1700.

Since Intel and AMD are both 64 bit (Core 2 Duo) that really isn't an issue anymore. So it comes down to
Budget
Overall system build quality (check the LCD, Keyboard, Chassis etc)
GPU desired with the system
Personal preference

If it is between a Core Duo and an X2 go for the X2, the core duo's are 32 bit and have a slower fsb than either the C2D or the X2 (by far on the X2).
If it is between a Core 2 Duo 5xxx series and an X2, go for the X2 (The 5xxx series of C2D do not have the 4 MB cache and have abismal clock speeds).
If it is between a Core 2 Duo 7xxx series and the X2, go for the Core 2 Duo (4MB cache, plenty of clocks, manhandles the X2 in any and all benchmarks.)

Where an I find this benchmark information. I looked around the site and couldnt find anything.

I don't have benchmarks on all of them, I have a few.

This would be a Turion MT-40 vs. an old T2500 Core Duo, notice the CPU, memory & PCMark scores.

A core duo easily manhandles the Turion.
Here is some CPU vs. CPU info on Core Duo vs. Core 2 Duo, but you are going to have to draw your own conclusions, they are not direct comparisons. I am speaking from experience with all three CPU's.

Thanks for the info. Im still a little confused with the AMD cpus. I see that they have alot of Turion X2 Dual Cores. The Price of the 7xxx Core 2 Duo is more than I want to spend as I dont use my laptop for anything crazy, I save my desktop for that. Which X2s should I look at as you said they are better than the 5xxx Core 2 Duos.

For what you are doing, any of them will be fine. TL-50 will do everything you have said you want. Don't sweat the 256 kb cache compared to the 512 kb one, it doesn't matter with the onboard memory controller AMD uses.