I use the Lee 4 die set for .45ACP, in my Hornady LnL progressive machine, and get great results. I use Lee pistol dies for 9mm, .38, .357, .45ACP, .380, and recently for 10mm. I have been very pleased with all of these, they just plain work great.
I like the recapping pin design on the Lee sizing die, great design. Also, if you are using the Lee powder measures, their powder-through expander die is THE best set up (period). I still use the Lee powder measures over the (nicer) Hornady powder measure in some calibers, because the PTX works so well. The Factory Crimp die is also an excellent, fool proof design. Some people have problems with it resizing their oversized lead bullets, and getting some leading, but this has not been much of an issue for me, and does not matter with plated/jacketed bullets.
As for the Lee .45acp sizing die not working with the LnL, that's not so in my experience. It's close, but there's just enough length...
I do think that Redding are probably the overall nicest dies out there, but for most applications not really necessary. I load .44 mag with Redding Pro carbide dies. They are really nice, but the ammo produced does not shoot any better than the stuff made with my Lee dies. I believe that Redding makes the dies for Dillon (fact check, please, but I recall reading that...).
RCBS has always made nice dies, but I think the new ones are no longer made in the USA (fact check, please, but if so, I think this matters...). I don't have experience with Hornady dies, but I'm sure they are good, as Hornady puts out a good product.
Like someone else said, any quality die is going to make good ammo...