I have both so I tested them, due to AoA being at maximum heat I had to test Fiery Atomizer CTR Max vs. AoA CTR VH.
Measured from when the charge bar appeared to when it disappeared.
Ash of Agni had an average of 126 frames@60fps (2100 ms)
Fiery Atomizer had an average of 102 frames (1700 ms)
might be off a few frames but the 4* one would definitely be faster at max heat compared to 5* unheated. But, the AoA has a greater range so it might be worth heating it to at least level 5 first, or use a trinket.
I don't know, because I haven't had the 4-star version in a long time. But the Bombing Guide lists bomb charge times in milliseconds. If you can time your 4-star's charge, then you can compare it to Ash of Agni, before you own Ash of Agni.
http://wiki.spiralknights.com/Bombing_Guide#Bomb_Charge_Time