Intel has long ruled the laptop world. They can provide a whole "platform" all by themselves, chipset, networking, wireless, CPU, all designed to work together, and as a single brand name, Centrino. Intel also sells more graphics chips than anybody else, because their graphics are integrated into the vast majority of laptops. AMD is a minor player in the laptop world. Many companies have only recently started using AMD chips in laptops, and desktops. Part of that is just because AMD is smaller, and so has to focus more attention on desktop performance, so mobile processors were only slightly tweaked versions of desktop chips, and there were few of them.
Turion almost certainly performs better than the original Pentium M used in the first Centrino models. Now, I don't know. A Core Solo is undoubtedly going to give you lower performance when using anything multithreaded, compared to an X2, but a Core Duo probably competes quite well.
Tom's Hardware is one of the few reviews I found that had reasonable comparisons between other chips, instead of just reviewing a Centrino against another Centriono.
http://www.tomshardware.com/2006/08/22/..._core_laptops_have_arrived/page12.html
The Turion and Core Duo are what I'd call equal to each other overall, at the same clock speeds. However there are some applications that perform significantly better on one or the other.
The Core 2 Duo mobile (Santa Rosa) platform (still branded Centrino if a laptop uses all the Intel components required) should provide consistently better performance over the Turion X2.
The Centrino line overall is extremely low power.