So I hope it's OK for me to add another post to this thread even though no one else has posted since my last post. I just reviewed the rules and posting guidelines and didn't see any rule against it and since it's been a couple days, I wanted to make a new post with this new information.
I've been burning in my SR225's for a couple days now, 3-4 hours at a time. Since having their drivers replaced they sound different to me, so they haven't been useful for A/B comparisons between Duet / 5S / 4 since there's always my (obviously fallible) audio memory of what they should sound like. I'm now definitely a believer in the idea that burn in can change (and improve) the sound of headphones!
Anyway, point is that I went to my local hi-fi shop with both my iPhone 4 and 5S to audition some headphones, specifically the Grado RS2i's. It was a slow Saturday for them and they handed me the RS-2i's and set me up in my own room with a nice comfy chair. I spent the better part of an hour listening to the 2i's out of the 4 and the 5S. Sometimes going back and forth every 10-20 seconds on the same song, leap-frogging through it; while other times, I just relaxed and listened to one or more songs at a time, back and forth. And my conclusions are the same as with the SR-225 (but less complicated by the replaced drivers / memory of what they should sound like issue): the iPhone 4 does a better job with the bass in both the 225's and the 2's and the Senn PX-100's. The 5S, however, handles all the rest of the spectrum better than the 4, I think. And it seems to have more authority, more ability to handle loud and complex passages. It is more detailed (maybe what some mean by more "digital sounding"). It is more analytical, clearer, more precise. For me, these are all good things. In the case of the PX-100's, these things are not enough to outweight the bad bass. In the case of the 225's and 2's, it's a wash, but I would lean towards the 5S as being the winner.
What is not a close call, however, is the A/B testing with the Sony MDR-7506's. The 5S does everything better than the 4 with these headphones. I didn't need to go back and forth and relax and use tricks or have my wife switch randomly between the 4 and 5S (blind testing, IOW). Clearly the advantage went to the 5S. Everything was better. I suppose if you like softer, more laid back presentation you might like the 4 better even with the 7506's. But, my taste runs more towards the opposite end of things. I did the 7506 testing at home, BTW, since I already own those.
So, I was just about to leave--talking with them about 2i vs. 225 direct out of the iPhones (they really need an amp, both of them)--and then I saw that they had a single pair of Sennheiser HD-595's on close-out. They used to be a Sennheiser dealer but apparently Sennheiser changed their rules for dealers and this place didn't want to deal with it all so they have been slowing getting rid of the Senn's. Well, this was their last pair. I said, "what the heck!" and asked if I could try the 595's.
WOW! Talk about synergy! Very quickly I was loving these phones paired with my 5S. And once again, as with the 7506's, everything was better out of the 5S than the 4. Curious, I went on line and checked the specs on the 595, confirming a suspicion I have had all along. The 595's have a nominal impedance of 50 ohms. The 7506's have a nominal impedance of 63 ohms. Both are very efficient (118 dB/V and 112 dB/V, if I remember correctly--I had to convert the 7506 spec from db/mW--I don't have my scribblings in front of me--but it was in that range).
Anecdotally, so far I'm finding that the 5S really shines with headphones with 50+ ohms of impedance that are still efficient enough to be driven to reasonable volume.
YMMV, of course, but this is my suspicion. I think testing 16 ohm IEM's with both would really increase this issue, tipping clearly to the 4's advantage. I still think all this has something to do with the output impedance difference.
And on that subject, I'm tired of waiting for someone else to do a measurement of the output impedance of the 5S, so I'm going to measure it myself at work (I work at Cornell's particle accelerator and we have plenty of oscilloscopes sitting around, as you can imagine, as well as an electronics shop full of resistors--I just need to buy the adaptors needed for the job). Stay tuned. Unless someone already has done the measurement, in which case, please post it here!
Anyway, I walked out of the hi-fi shop with the HD-595's for $160 which I thought was a pretty darn good deal. I've only listened to them for 4 hours or so thus far, but I'm really liking them--straight out of my iPhone 5S. They're not as bright and edgy as the 7506's, but still have great clarity and brilliance, great bass, nice mids--just my first impressions, though, but I'm happy to have a decent pair of full size Senn's to experience. And I'm glad that I won't need to go to an outboard amp or dac/amp combo. At least not until and unless I want to.