While I have enjoyed cyclical initiative, I'm starting to be convinced that 2e's system for initiative made for a better balanced game.
AD&D did a much better job than latter editions of treating the turn based system as an abstraction of real time combat.
1) In 3e, when ever you take your turn, all other activity basically stops and everyone becomes frozen in place. You then have 6 seconds to basically do whatever you want without any interruption. Regardless of what you do, everyone has to stand there and watch you do it. In theory, this is what AoO are supposed to prevent, but in practice its too easy to take a 5' step or something and the opposition is frozen in placed forced to watch you.
2) In earlier editions it was possible for two characters to hit each other (and even kill each other) at the same time. In 3e and latter, you never get that Rocky vs. Apollo, Arthur vs. Mordred, Rand vs. Ba'alzamon, etc. trope.
3) In earlier editions, if characters had multiple attacks in the same round, they alternated attacks until they ran out. You couldn't make 3 or 4 attacks on a target before it reacted unless it was suprised. Instead, you made attacks, and then you got the rest of the attacks later. The dragon went 'claw', and then it went 'claw' and 'bite' later. D&D has always had a problem with initiative being the most important dice throw of the combat, and 3e tended to make the problem worse.
4) In earlier editions, you started an action at one point in the turn and completed it at a later point. For example, you resolved movement while opponent was moving, and then after moving you resolved attacks. Or, you started casting a spell and then sometime later in the round you'd finish it. Between starting it and finishing it, things could happen to you.