Always hated the measuring system for best weapons cause it doesn't take into account having a bad luck string of misses/evades I usually like taking the average hits from a long fight to see what would be better.
Just using the numbers you got in the screen shots taking the average damage from each bow it does seem like the Shining Longbow is the winner. With this math though its not taking into account misses/evades/resists which would be different for end game raid bosses and event mobs also left out the flaming arrow AA buff and just compared the bows. The difference between the weapons is a lot smaller then what you were able to show because in your test it seemed the Frozen Bow missed a whole lot more which could be just due to some bad rng. This math wouldn't work with weapons if they had different mod% but since both bows have 5% archery mod it should be equal.
Oh also forgot dunno what buffs you had during the measurement. Haste will usually help out higher damage longer delayed weapons a bit more then low damage lower delayed weapons. Though I'm just guessing you already have your haste epic equipped in your charm slot and had the lonely shaman buffs active at the time so you were either maxed or close to maxed haste.
Frozen Bow of the Gelidin Average hit is 1275 x attempts 231 = 294,525 /time 360 = 818.125
Shining Longbow of the Leviathan Average hit is 968 x attempts 303 = 293,304 /time 361 = 812.476 + the proc average hit 207 x attempts 81 = 16,767 /time 361= 46.446 = grand total of 858.922
Any mobs with high magic resists or immunity to magic it would be better to take the Frozen Bow. If your able to land magic on the mob easily then Shining Longbow is the way to go. Cant go wrong with either one though really.
