I have tested through quite a few tanks of each 87, 89, and 91+ and I can say that 89 seems to be a sweet spot for my truck. I could not see a difference in my MPG calculations, or my butt-dyno, between 89 and premium. However, when I went from 87 to 89, I see smoother idle, smoother acceleration, and 1-2 mpg better fuel economy. It more than makes up for the extra $2 per fill up.
I do not have a tune, but have spent significant time reading everything I can about our engines. Black Bear Performance seems to be one of the best when it comes to tuning our trucks. Therefore, I think I would trust them and their advice on this subject. They have the following info in the FAQ section of their website.
2007+ 5.3L engines. At 10:1 compression, this engine (all variants) cannot run efficiently on 87 octane. Power output and mileage will be noticeably better in 95%+ vehicles simply by switching from 87 to 89 octane. 91+ preferred.