In terms of sound quality which would win?

And If you already have the iPhone 4s, would the gap in quality justify also buying the Cowon J3? Or just stick with the 4s since you already have it.

Bump

I think the differences come down to whether or not you like to use an EQ, and how well you like the sound of BBE processing, and oversampling. If you use an EQ, Cowon is pretty much tops when it comes to portable players that have great EQ features. If you just want something that sounds 'normal' then a mobile phone with no hiss should do it.
 
Personally, when I went shopping for a DAP, I wanted something that sounded as powerful and full as my old Sony stereo at home. With some of the subtle EQ settings on my Cowon S9, I can't distinguish it from the said stereo. Throw in some crossfeed with the BBE Viva setting, and I think the experience is second to none. Just like with the OLED screen, once you listen to it and get used to the color saturation and vibrancy, it's hard to find something as pleasing.
 
Before landing on the Cowon S9, I was using an iPod 5.5g, back when they had nicer Wolfson chips in them. I installed RockBox, and messed with the setting a lot and loved them... then I heard my friends player (an S9) through my headphones and his. The iPod was returned shortly thereafter.

Or get the iphone 4/s and get the BBE app

I have the Cowon S9(same sound as the J3) and the 4s and I find that the 4S has better soundstage separation, bass and dynamics but a hair less treble presence when compared to the S9. Both sound nice but like Steven says you can customize the Cowon far more. Also, the battery life on the 4S is horrible, especially if you use it for long commutes while listening to music. I also prefer file drag and drop over itunes, for these reasons the S9 is my primary player.
 

The 4s has better Instrument Seperation in my opinion. The cowon has a better treble presence though. Try them both out and see what you like. It all comes down to personal preference.

As expatinjapan said, there is a BBE music app in the IOS app store called SonicMax Pro.  Got it myself a few days ago for my ipod touch 4g and been enjoying it.

both are excellent players.
 
the iphone 4/s is actually a competent player, so you won't see a difference in sound quality.