AAdvantage is hard to beat.
Low redemption rates (20,000 one-way US-Europe, South America during off-peak dates)
Good award availability even for off-peak saver awards
No fuel surcharges on AA
award tickets and partner flights except on BA
As soon as you reach Platinum status, you get double the miles on your travel (although the extra miles don't count towards elite qualification)
If you really travel a lot (over 100,000 miles a year), you will get Executive Platinum status and you will get unlimited complimentary domestic upgrades based on available space, plus 8 Systemwide Upgrades (SWUs) that can be used to upgrade to the next class of travel, even on long haul flights
If you're more concerned about getting free US domestic upgrades faster, then UA
Mileage Plus or Delta SkyMiles might be a better choice, since you would be eligible for that at lower tiers. AA
only gives out a finite number of upgrade stickers for their Gold or Platinum members.
If you are concerned about lounge access, then Aegean's Miles & Bonus program will get you Star Alliance Gold Status at the 20,000 mark.
The biggest mistake made by most human beings: Listening to only half, understanding just a quarter and telling double.