Now I have to say this...This is my "very first" Wizard chest set item since I've been wearing Zunimassa's Chest for well...2 years or say since I hit level 60 a long time ago on my Wiz.
I have "not" found any wiz related set item chest sets since day 1.
That means I haven't even found a Tal Rasha chest at all, even to this day.
But what I wanted to say is comparing Wizard sets now that RoS is released:
Vyr's Astonishing Aura chest versus Tal Rasha Relentless Pursuit versus Firebird's Breast
Tal Rash will always guarantee 4 primary affixes and 3 sockets...but one of 4 primary affixes will always be IAS between 5.0-6.0%
Now Vyr's chest will always guarantee one of the 4 primary affixes will be CHC 1.0-2.0%.
The only problem with Vyr's chest is that you don't get the guaranteed 4 primary affixes and 3 socket advantage like Tal Rasha chest does.
The only thing the Vyr's set has an advantage over Tal Rasha set is that it rolls some seriously high Intel and also the first set bonus is 500 Intel.
Now Vry's chest can't enchant AR on the one I've found, but it begins to make me question if it can do a random roll of AR at all.
But I don't know about Tal Rasha chest if you can get random roll of AR on it.
But thinking back the AH days I think there were some Tal Rasha chests with AR on them that I saw on the AH.
Also for other Wiz chests the Firebirds Chest is for Wiz only but it will guarantee roll Intel and AR.
Now comparing between Vry's chest and Firebirds chest they're both good chest but if you want AR then Firebirds is the way to go if you want a Wiz set item chest.
But Firebirds is sort of a fire build set.
But looking at all the Wiz sets it seems other items in the Vyr's set is good for CHC since both the chest and gauntlets roll CHC but the gauntlets roll better chance of CHC.
Vyr's set is only a 4 piece set which a lot smaller than the Firebirds set and Tal Rasha set.
Which makes you think you can combine both sets together if possible.
Combining Wiz sets
Vyr's set with Tal Rash set can go well together since Tal Rasha set has belt, amulet, offhand and Helm to which Vyr's set doesn't have.
Though combining Vyr's set with Firebirds set will be a bit more difficult since you won't be able to get the full sets of both.
You would have to choose which of the sets you want to complete or just have two Wiz toons with different builds would be better off.