Well, the upcoming release for Wrath of the Everchosen shows that my move to AoS is ordained by the gods! Rejoice!
As for these replies, you guys are the duck's nuts! All of this is so helpful. I'll break down my thoughts.
General: I'm pretty loose when it comes to play style, and I tend to enjoy it all. So it really just comes down to basic functionality. As for the individual armies, I'll break down my thoughts, based heavily on your suggestions.
Nurgle: It seems that people are not really excited about this. I do appreciate that it's a user-friendly army, being tough, and of all of the Daemons I have the most of all of these. I'm even one of those weird 40k players that has a bunch of Beasts of Nurgle. Reading around these forums, I see that the thinking is that Nurgle are barely functional as a whole Battletome, let along gimping oneself just to Daemons. Also, as I ran the standard recently-nerfed Chaos soup list in 40k, with a heavy dose of Plaguebearers, I'm a bit tired of not killing anything, and just letting waves crash up against me. I might, then, give my stinky boys a bit of a rest for the moment.
Khorne: Well, I am a dyed-in-the-wool Khorne boy. When I got into Warhammer in 2004 I ran pure and exclusive Khorne in both WHFB and 40k. Lost every game. Was great. I also think my Bloodthirster is the best model I've ever painted, and I don't even mind having 2 Greater Daemons with them, as Skarbrand looks so different from the normal model. I've been thinking of buying him anyway, and I'm glad to see he's actually good in AoS, unlike 40k. I did have the received opinion that Mortals are where Khorne shines, although I see on the tactics thread here that the opposite opinion seems true, with people saying Mortal Khorne needs a buff. Any further insight on this would be great. I do love me some Khorne, and if they are functional (mid-tier or just below) I'd be interested to hear. I could bear throwing in a Mortal hero or two. That would hardly break the bank, and the models are just beautiful.
Slaanesh: I see what you're saying with the models looking a bit same-y, but I've never come across in 40k anyone who plays Slaanesh ever, besides me, so I still think they look great. I do vastly prefer the old Daemonette models, but seriously ****** those things, as their arms will never stay on. But the grab girls have their charm. I can stand getting a second Greater Daemon, but I would build her as Shalaxai. Would the army be doable with 1x KoS and 1x Shalaxai, the received wisdom being that you need 2 KoS? Currently they're coming a near second in my thinking, but that could change with your input!
Tzeentch: Obviously the LVO results show that Tzeentch is functional with pure (or near pure) Daemons. I should also mention that, playing 40k, I have some Arcanite models, in bird-gors. And just to add some variety to my line-up of DPs, and because I dislike the Herald models, I have an Ogroid and Gaunt summoner on and off disc. So I have many options here. I have no interest in, and a distaste for the meta, so I won't be running the list that will hopefully be nerfed. But that LoC, flamers, and horror are strong makes me happy, as this is what Tzeentch should be about. For now I'm thinking of starting here, just to learn the ropes, as it's always good to start with a functional army. My worry is that it's a shooting/psychic army in a melee game, so might not be representative of AoS in general, and so not the best intro.
General Again: One further question: I don't really see people running DPs, which is odd to me, as they're basically the only good unit Chaos has in 40k. Is there a reason for this? I do love my Princes, and have plenty of them, and was particularly hoping that they could substitute in for those extra Greater Daemons which I'm so averse to getting. I will mention that my aversion to multiple Greater Daemons is that I see them as centrepiece models, and mathematics necessitates that you can't have two things in a centre. Which is to say that they should be striking, and more than one makes them less so.