Time in Game
I have been playing since 2017-September.
Loot Tier 9
As Kerridoc says, Titan loot tier 9 gives 3 ascension item rolls per Titan. So average +50% more 3* items.
Since my alliance fights 5*-6* titans ( we keep losing teammates to Real World sheet and I really really like my teammates so alliance shopping or Mercing are not happening) I usually get 2 ascension item rolls per Titan.
You cannot unlock classes on 4*/ 5* heroes without 3* ascension items.
Rare titans
So far 1 bonus roll on a rare titan for 1 Tabard. As others have said, rare titans are fun break from normal titans but not a significant source of ascension items.
Titans are the object of the game
Empires is all about the maximum 380 Titan kills per year ( for me 780 rolls, actually less since ours can escape, for a player at loot tier 9+ at least 1,140 rolls, maybe less with introduction of rare titans and higher star titans ).
War is only 104 rolls per year.
Challenge events only 24- 60x 3* per year.
I do not recall the frequency of rare quests but I would be surprised if five times per month.
Seasonal events 5x 3* per year.
So killing titans is king.