I've tried both, so here are my impressions:
Bass/Mids: s4i is superior, but the AIEM's aren't bad.
Treble: AIEM is superior. The s4i sounds very harsh in the higher ranges. In fact, this is such a glaring weakness with the s4i, that I cannot recommend them because of it. Now, many have stated that these IEM's need a great deal of burn in time to loosen up, so I have given them another chance. Out of the box, the new ones are harsh once again, but I'm in the process of breaking them in. We'll see if it improves.
Tap Control: s4i easily wins - there are little buttons to help with the tactile feel.
Wire: I hate the 'rubbery' feel to the apple wire, so s4i wins there as well.
Comfort: there's no debate on this one - the s4i is EASILY the most comfortable pair of IEM's I have ever tried! That being said, the Apple's might be second, but they are second by a wide margin.
So, in summary, the s4i's are just about perfect and would be a great deal at $99, if not for the fact that at any reasonable volume, the harshness in the treble makes them almost unbearable. Many have agreed with me on this, but there are some who disagree, and still others who agree, but who say it gets much better with burn-in.
I hope this helps.