Myoface,
I am sure that is a difficult decision, but my advice is unlike others. We all send out are applications to different companies and wait for an ananswer. You are in a very unique position having two great airlines offering a job. My advice is go with one you like most and commit to them, dont be a ride the fence kind of guy. Why do you think some airlines wont hire people with a 737 type, because they know when SW calls you are gone. I dont think anyone would notice or care if you went to AS and then left to go to SW 6 mo later, but I dont its best. DO what is best for your family and hold on to that integrity.

Good Luck