Well I am new to the Turion so I will let someone wiser tell you about that but basically I know a bit about the power consumptions of each. If you want I can show sources, but off the top of my head here goes: The Turion exists in 35W and 25W versions, with the greater power consuming one being somewhat more powerful to use an inadequate term to compare the two. The Centrino started off with 27W and 12W versions and is now at 21W and 7W for the regular LV Pentium M and the ULV Pentium M respectively. LV=Low Voltage, ULV= Ultra Low Voltage
The LV lines come in speed between 1.6 and 2.0 ghz nowadays IIRC (although older versions were lower clocked) and the ULV is currently between 1.1 and 1.2 ghz. A 1.6ghz Pentium M will outperform a 2.8ghz P4 in some tests. Yeah, they are that good.
So, correct me if you think I am wrong and I will then check my answers and someone please explain a bit more about the Turion which as I have heard is actually a 64bit CPU.