The only way to really know is to compare them yourself (if possible). While I haven't tried the J3, I did own an iAudio7 for quite a while. It has the same BBE and EQ enhancements (maybe a generation older) - but was very well regarded as an excellent DAP for SQ. I loved it while I had it.
I'll add at that point that although I'd never really tried much in the Apple line, I basically discarded them as 'mp3 players for the masses' - and smugly assumed that because I had a Cowon, I had a superior player.
Skip to late last year. I had to cash some reward points (expiring), and one of the options was the iPod Touch 4 (32Gb). Thought I'd try it - in the end glad I did. ABing them side by side (flat/no EQ) - for me, the Touch sounded as good (if not better) than the Cowon. Add in the wifi, bluetooth, available apps, gui etc - for me the Touch was better. And this is especially so with the Equalizer app - at adds a decent parametric equalizer that was sorely missing. I only ever use it on my SE425 IEM's to give them a touch more sparkle - but it makes a difference.
You will find fans on both sides Cowon/Apple who will claim the product they use is much better. The secret IMO is to take more note of those who have actually owned both (there are a few on head-fi).
I put them both on a par SQ wise.
Cowon has slightly better EQ ability - but negated now by the Equalizer app. The Cowon's also have better battery life, and expandable memory. It also has support for more audio/video formats.
The iPod Touch G4 has wifi, better apps. I find it's battery OK - and 32GB is fine for me using 256 AAC (currently have ~ 260 albums onboard). If you use lossless (I did for a while) - you can use ALAC (simple transcode from FLAC). The Touch also has a line-out, so you can bypass it's internal amp, and get a cleaner signal straight to a portable amp (the J3 doesn't).
But if most important thing is the sound - IMO it's a wash - both are very good DAPs. Take your pick based on the other features.