Of the ADDIEM and the S4, I think the S4 is a more fun phone, as the ADDIEMs, which I do like a lot, are more detail-oriented (mids, highs) and less bassy than the S4. If you are CONUS, you can get the ADDIEMs from ebay for $44 from a seller called 7Dime. Perfectly legit ADDIEMs, B box is what I think. Not really used. I've acquired like 9 pair (5 from 7Dime) from $30-39 for various friends and relatives (teenage daughter has two sets, backups you know).
Anyway, given the choice with the iPhone/Touch, I would say either is good, but the S4i will have more bass extension. Again, remember to burn them in. I know it sounds crazy, but they do change for the better (treble calms down).
Hope this helps.
Did you read the ADDIEM thread? Some folks with very good IEMs are big fans.