I don't think your problem is AA, it's Laguardia! That's a horrible airport to fly out of, but you may have little choice. And when the weather is ugly in the Northeast, it doesn't matter who you fly or where you fly from.
My experience with AA has always been great. A couple of years ago I had 29 consecutive segments that were either on-time or early. But those were flying out of Miami, mostly non-stop or through DFW.
I have also found that when air travel really goes in the toilet, American always finds a way to get me home as expeditiously as possible. That's not always true with other airlines, although you will probably hear horror stories about any airline. I'm also sure my frequent flyer status with AA helps a lot.
I was returning home from Philly on AA a couple of years ago and a colleague was returning from Philly to Austin, TX on Delta. The weather was horrible, and no airline could do anything about that. But American got me home that night - 1 AM, but home! My colleague called me at 4 PM the next afternoon and told me she had just walked in the door! She got stuck in Atlanta overnight.