I have not driven one of the new 5.3's but have read and talked to people who say they are noticeably better/peppier than the previous models. I would still expect it to lag the 5.7 tundra a little.
As I understand it the AFM problems have been quieted down greatly, but if your planning on keeping it to high mileage I think the tundra would be a safer bet than AFM. My 2011 with AFM I sold to my uncle is still running strong at 75,000 with no problems, but it uses a quart of oil in a 5000-7000 mile change which I attribute to AFM.
I can handle 5000-7000 but have heard that a qt every 2000 is not unusual. It is going to come down to price. If I can get the Tundra low enough to offset the MPG diff then it is the Tundra for sure. If equal in price decision is tougher. Chevy might make the decision easy if they chose not to give me the loyal customer discount. I got a good deal from Moritz but it is $1500 better with the discount. I am not going to subsidize current owners and told them that so we will see what happens. Now $500 would not be a big deal.