Bump.... Yeah, I've had this exact question recently as well!!!
Just bought a 30Gb iPod 5.5G on eBay, as I was having difficulty installing RockBox on my 6G 160Gb classic due to its CE-ATA drive. So, I'll report back when I get my new iPod, RockBox it, and have some time to listen to them both.
So... Let me start off by saying that I am by no means an audiophile, and this is my first opinion/review type post. So, take it easy on me... I have been a musician and around music since childhood. So, I know what good music sounds like, and the natural intonation and timber of many instruments and voices...
First off let me say that these are very close tonally. So, at a first quick listen, after equalizing the volume output from both sources using a 440Hz sine wave pure tone and a SPL meter, it is difficult to distinguish between the two. (Unlike the 6th Gen Classic, which is easily distinguishable, and sounds terrible in comparison!) However, after a bit more time and some critical listening, you can begin to decipher slight nuances between the two.
Overall I would say that the sound from the 5.5 Gen iPod is "natural" and "full". Where as the sound from the 5s feels slightly "narrow", "compressed", and "forward".
So, if I was pressed to say which one I like better, I'd have to say I'd probably pick the 5.5 Gen iPod.
To describe some more of the subtle differences, I'd say that the 5s has slightly punchier bass, however it appears to linger a bit too much making it sound slightly "loose" and a bit unnatural. The 5s also has a bit too much emphasis on the upper bass to low mids, making it sound a bit bloated. The iPod definitely has a better mid section, where as the 5s feels a bit recessed, this is probably the biggest factor making the iPod sound a bit more "warm" as I believe most world refer to it. However, with definitely present mids, they are not harsh. The iPod does a great job of making the mids smooth and natural. I think this also helps to add to the perceived depth of sound stage, it's open and airy feel, and it also helps strings sound much more natural. I also feel that the upper mids to the lower end of the treble are a bit more well defined, leading to a more natural timber and fullness to female vocals on the iPod. I will say that the 5s does have slightly more crisp upper mids and lower treble, which can both add some clarity and make that highs a tad too harsh. (So, I could see how some describe the Cirrus chips as fatiguing with extended listening sessions) For instance, when listening to several Eminem tracks, the 5s did have a sharper, crisper character to the vocals, however, the iPod still sounds more natural. This also makes many guitar riffs on the 5s a bit sharp on the attack, but slightly unnatural sounding as there is no natural sustain, makes it feel a bit thin. However, when listening to cymbals, the 5s makes the highs appear to linger a tat too much giving them a bit of an extra sizzle that is not what a real cymbal sounds like. I think this is also what makes some of the other treble on the 5s feel a bit "bright" and "tinny" to me. However, with the slightly bloated bass and lower mids, it does even out the sound on the 5s a bit.
So, again, they both sound pretty good, and are fairly close to each other on a quick, casual listen. (I had my wife do an A/B test with me and she did not even know I was switching sources) But, they do have their differences. So, again, strictly based on sound (I would consider the most accurate representation of the natural sound to be the best sound), I would say that the iPod 5.5 Gen wins. But, on the other hand, the iPhone has so many more possibilities with internet access and the app store. So, much more practical. If you already have an iPhone 5s, but not an iPod 5.5 Gen, I don't know that I would recommend getting one unless you are wanting to upgrade the hard drive and carry around a large lossless collection (especially if you don't have an unlimited data plan for your 5s, as you can stream music to your iPhone). Otherwise, I'd say the very slight loss in sound quality is worth the practicality of not having to carry 2 devices around with you.
Hope that helps... If you have any questions feel free to ask!