Uh, what

? AD&D not complex? You may have felt that way after years of playing gave you a comfortable level of system mastery, but if you allow me to refresh your memory...
- To calculate whether you hit, you have to roll above a number. So far so good. That number gets lower as you level. Counterintuitive, but okay. You substract your opponents AC from that number. Wait, what?
- Magic weapons have a
positive bonus, which you
substract from your attack stat... Err?
- Magic armor has a
positive bonus, that you have to
substract from your AC. At least there is a pattern.
Okay, so your attack stat is 4, you wield a +5 sword, your enemy has plate (AC 1) +4, what do you have to roll to hit? So my attack stat is negative, and the enemy's AC is negative, so I add it, which brings my attack stat back into positive, ... Ok I give up.
Now, if you're a Wizard, you don't roll to attack at all, but your enemy has to roll against a number on his sheet.
And of course each class has its own XP progression.
You roll initiative every turn, and it depends on things like which level of spell you cast.
To cast your spells, you have to keep track of ... bat guano.
Forget about using that magic sword you found immediately, the wizard has to take an 8 hour break and burn a 100 gp gem to identify the damn thing. At least he doesn't have to roll a spellcraft check. Uh, that item was cursed? Pointy hat spent 8 hours analyzing the matrix and didn't notice? Let's all rest another 8 hours so the cleric can pray for remove curse.
I'll stop here. AD&D was incredibly complex, but in a "watch out or I'll screw you over" kind of way. And in a "scrap that who cares about material components anyway?" kind of way. And in a "unified mechanics what's that?" kind of way.
3rd and 4th edition simplified and streamlined a lot of that. The core rules of the newer editions are much simpler and more streamlined. What makes 4th edition more complex in play are not the rules itself, but the tactical options you have and the interactions between PCs.
In short, AD&D complexity and 4th edition complexity is very different, and it's not the 4th edition rules that are complex.