The specs for the 2 laptops are almost identical (with difference in hdd capacity). It's a choice between the 2 CPUs.
The Turion is designed for mobile computers and gives you longer battery life (still not much). The only other advantage of the Turion I can think of is that it supports Intel's SSE3 instruction set (will benefit if a program is optimised for SSE3 - not too many of those programs at the moment).
Otherwise, the Athlon 64 3400+ has a clock speed of 2.2 GHz and 1 MB L2 cache (compared to the Turion's 1.6GHz and 512 KB L2 cache). I think you will find the 3400+ a much faster CPU.
Between these two, if mobility and battery life is not an issue, the 3400+ would seem a better deal (but it's going to be hot!).