I've got to be honest, I'm kind of torn between ARURF and ARSR. Thing is, I love random pick modes because it gets me playing champs I wouldn't normally touch. ARURF has the fast paced, action packed features of URF, whereas ARSR bring some challenging situations to "standard" play (which is something I don't normally touch).
Doom Bots was definitely better when you could vote for the level. From what I played last weekend, it's permanently set to 100 (which is weird, since that was Riot's issue with letting players vote [because apparently "too many players" went straight for 100]). I don't know if there was some bug with it, though, but it was definitely harder than 25, which is apparently what the Teemoing is set to.
Honestly, Siege is always fun when it comes around, as is Hexakill and OFA (in my opinion). Not something I'd play consistently if it were permanent, though. I liked Nemesis, and I think it would be fun to go back to that every 4-6 months or so. Ascension and LotPK were fun at first, but they've become so... Bland, for lack of a better word. I see them on the rotation now and just think it's not worth it.
From what I understand about Blood Moon and Dark Star, they were just Riot testing out something different. The lack of popularity with them doesn't necessarily mean we wont see them again, but if we do they'll likely have a few changes (wouldn't be the first time that's happened with a mode). Personally, Blodd Moon was just terrible. It was boring, repetitive and seemed to require minimal skill. As for Dark Star, that got repetitive really fast. Three games, and both icons, and I was gone (as were my friends).