Short answer: If you can deal with the price and bulk, the Algorhythm Solo will give you the best sound.
Explanation: The iMod's Line-out signal has the signal go through the iPod's internal DAC and out the Line-Out (and then through some capacitors). This makes a very clean signal, great for use with an amplifier. The bottleneck of the iMod is the internal DAC. This DAC is great for portable audio, but not so great when everything else in your rig is top-notch. For example, one rig that some people own is an iMod -> Some top-notch iPod LOD -> External Capacitors (V-Cap Dock) -> RCA Interconnect -> LISA III -> headphones. Assuming they have good headphones, the weak link is the internal DAC.
The Cypher Labs AlgoRhythm Solo bypasses the internal DAC in the iPod. The Algorhythm Solo supposedly (I don't know) has a high-quality DAC inside it. But what makes the AlgoRhythm Solo really awesome, is that you can output a digital signal. If you use the AlgoRhythm Solo with the JH-3A, you will be feeding the JH-3A the best possible signal. The signal won't be damaged by bad DACs, amps, etc. Everything would be top-notch. If you rockboxed your iPod, you would be able to play full 24 bit songs. If you input an analogue signal into the JH-3A, it just converts it back into digital for use with the DSP. So if you don't want to damage the signal, you will input digital.
Pros: You can have up to 240 GB of the best portable audio (so far) with a great user interface.
Cons: You will carrying around 3 boxes costing about $2500.
Edited by violinvirtuoso - 8/6/10 at 9:43am