I did the math assuming cd reduction based on getting cdr on items (which only affects dps on e) and assuming cdr of e based on the attack speed of the individual camps. W is still higher damage per second, and amumu can gank level 3 regardless of which path you go. The only influence path has is speed of clear, minor damage reduction, and some minimal burst damage (if you don't stick to the target long enough to get a second e off then the instant damage of e may out weigh the damage of w bc of the short time given to deal damage).
So what it comes down to is whether or not the damage reduction and burst of e on ganks out weighs the increased clear speed of w. In my experience amumu doesn't really struggle w/ sustain after the first clear or two, so if you get a successful gank off to buy some early armor and make monsters not a threat, e loses value. Additionally, amumu isn't an early game pressure jg. He can gank at level 3 but it's never going to be as good as an elise/lee/gragas level 3 gank. If we assume his strength is mid to late game team fighting, then getting the gold to be able to buy things like rylai's and liandry's in addition to tank stats becomes a huge advantage. Therefore, being able to farm jg camps on cd and gank at the same time becomes possibly more valuable long term than an increased early burst on ganks. (This is especially true if your lanes have any cc and you can for sure lock enemies down to get w damage off in ganks.)
So while yes he has the defensive steriod and the when hit cdr, I'm still pretty sure that if I did the math right then the original question (which mentions the defensive steroid) of farm speed vs dmg reduction and burst value is still a valid question.