For context, like most on this board, I'm just a hobbyist, not a pro. While I don't really play as much or at the level of a pro, I do play a lot (~10 hrs/week) and have been playing for a very long time. And I do have very high standards when it comes to my sound. So I'm very picky about my reeds.
I don't actually play my favorites very often. I love Rigotti and BSS, but I can't usually afford them unless I find some NOS on ebay or from a private seller. LaVoz and Rico are a close second for me but much more affordable, so that's what I've played most of my life. Never played a Vandoren I liked on sax, although they're my favorite on clarinet. I hear Gonzales is similar to Vandoren, so that's a non-starter for me. I do play a few synthetics, usually when I'm doubling on clarinet. But that's another thread.
As for different classical and jazz reeds, the reeds I typically play are a bit too warm and buzzy for the ideal classical sound. So I tend to go up a half strength for classical sax. On clarinet, I can comfortably play the same reed and mouthpiece for both.
Consistency? Cane being a natural product, consistency is really going to be impossible. I've found this to be true on all brands. Anyone who plays cane is just going to have to accept this reality and deal with it. I deal with it with my pocket knife.
TLDR, my favorites, considering budget, are LaVoz and Rico (orange/brown box). I like Rico Royal, but they tend to not last very long these days. Not a fan of Plasticover. Even though the OP doesn't care about strength, I think it's an important consideration. LaVoz med-soft is just a tad softer than Rico 2.5, so it's in the sweet spot for me (on tenor). I usually have to work on my Ricos a bit, and LaVoz, not so much.