I'll start by saying I'm a firm believer in Aggressive AI and only play with it.
With that said, I feel as though Normal AI is more of a builders game, I also find that more of the older players enjoy this setting while Aggressive AI is more of a warmongers game and find that more of the younger guys like it.
Not to be stereotypical I just find the younger players like the constant warfare more and the older "dorkier"

sorry sorry lol players enjoy more of the micro management slow builder type games hehe.
The reasons I find Aggressive AI superior is simple, as a warmonger and rusher, no matter the map I'll rush and take my continent or most of it leaving a trade partner at most, I find that normal AI can't hold its own, I find it completely without challange and found myself going from noble a few months ago when I bought it straight to Monarch, as soon as I switched to Aggressive AI I got stopped in my tracks at Monarch and started finding the game very challenging.
The AI's could finally handle my warfare, and the new BtS has helped since it has improved the warfare of the AI imo.
Normal AI it just isn't there, it can't handle war and when the only victory condition you want is the total submission of the entire planet it's no fun. I also find the Aggressive AI declares war constantly on eachother as well as the player which I find more realistic.
How many civs go 1000 years without a war..
Aggressive AI techs slower but it fits into my game better, even with the faster pace of teching in normal it just gets destroyed and once you have a continent to yourself it's kind hard to stop you.
It's also offset by the fact that you tech slower unless your a god in diplomacy.
I also find your statement about the cottaging completely false, no offense at all but with BtS I've seen the AI do nothing but cottage spam everything and they usually have cities that are 18+ by the mid-later parts of the game.
I also think your handicapping the AI's to a certain degree by using random personalities, the civs traits and uu/ub are built up around there personalities and they are most effective by there individual leaders, by using random personalities your mixing a leader personality that doesn't play to its strengths.
Aggressive AI also lets me worry less about micro managment and focus more on the apsects I enjoy like the actual game-play