Line-outs should be better than the headphone-outs. So the end results should be better this way using LOD cable yes..
Line out using that LOD cable completely bypass the Ipod internal amp and let you use whatever external one of choice.Just feeds a straight signal from source( Ipod ) unaltered by internal Ipod volume potentiometer/control and/or internal Ipod amp circuitry.
This actually isn't true in general, and definitely not true on the iPod classic as evidences that you can adjust the line out volume in software by varying the line out amp gain. You can't actually get an unamplified signal out of a modern digital device. The internal current sources are simply not strong enough to drive an analog signal off chip. If you can get it onto a wire, you're going through an amp.
Instead, a line out and a headphone amp use different kinds of amps. A headphone amp requires a high power, high quality amp because it drives a low impedance load with a lot of reactance. These are expensive and use a fair amount of power. A line out in contrast drives a high impedance, mostly resistive load, therefore it can use a cheap, low quality amp. Aside from the power/cost of the amp though, theres not much difference. If you put both into a high impedance load (~1kohm), you will get essentially the same output. The line out is basically just a way for the vendor to save money on the second set of outputs.
As for which you should use, it depends what you want. If you want fixed, line level voltage, the line out is probably easier. If you'd like to be able to control the volume (and don't feel like hacking up rockbox to do it), then use the headphone amp.