Like most things, you get what you pay for.
I've used both methods for 3" of lift and prefer full replacement leaf packs because they're made and shaped for the desired height with all the leafs having similar spring rates. They also netted a half inch more lift than the AAL's did.
Because the AAL's are arched differently than the stock leafs they get packed into, it's not quite a solid nested arrangement. They left different size gaps between leaves. They're also a thicker leaf with a dissimilar spring rate so their extra heft can bolster the stock leafs into more arch.
With that said however, AAL's can do the job for half the cost and do have their place in the natural order of things. I'd say if you just want to get a little more lift to run some bigger tires and don't have plans to do lots of technical offroading with heavy flexing, or even aren't planning to keep the vehicle long term, or plan to go bigger later, AAL's are fine and will serve the need.
A person who plans to keep their vehicle as it is for a long time and do lots of offroading would likely be better served by full replacement leaf packs.