And just to back this up with numbers…

Lets say we give both a double attack weapon and the chance to proc was 1/3.

Looking at the tower with 30 vet rings, Earl has 2583 damage. A rush with 3 attacks would have 1 proc of double attack. So:

3 x (2583 x 1.5) + (2583 x 1.5 x 1.5) = 17,435.25

Since Michonne only deals 2 attacks, I will assume we rush 3 times for the sake of simplicity. Earl will have 9 (3 rushes x 3 attacks) rush attacks and 3 procs of double attack, Michonne will have 6 rush attacks (3 rushes x 2 attacks) with 2 procs.

So Earl does 3 x 17,435.25 = 52,305.75 damage in 3 rushes.

Michonne:

3 x 2 x (2742 x 3) + 2 x (2742 x 3 x 1.5) = 74,034 damage in 3 rushes.

To be honest, that differs by a lot. Even without double attack, Michonne would do 49,356 raw damage from her rush, which is less than 3k short of what Earl does with double attack.

Looking at the regular attacks between the rushes, Michone makes up for that because she has higher base damage.