The LA cruise terminal is on the far west side of the Port of Los Angeles - in San Pedro. Its actually not too much further from the port terminal to LAX (19.5 miles) than LGB (15.5) miles. Both trips can be miserable at times. You say your flight is 11:15? On a weekday or weekend? Fighting the 405 at 8:30 am will not be a pleasant experience. Nor is Century Blvd. On the other hand, the most direct route to LGB means going up the 710 which, depending on the day and cargo ship arrivals, can be jammed with trucks hauling containers.
LGB is certainly closer and easier to get to, but AA's LGB schedule isn't as flexible on rebookings as LAX.