Not necessarily. I've compared three blowers, one gas, one corded electric and one battery powered unit below, using the manufacturer's published specifications:
Echo PB-250LN two-cycle gas handheld blower: 391 CFM and 65 dB(A) - I own this and it's very quiet (no ear protection required).
Black & Decker LH5000 (Leafhog) corded electric handheld blower: 385 CFM and 69 dB(A) - I own this and it's so loud that I need to wear ear protection.
Ryobi RY40411 (Jet Fan Blower) battery powered handheld blower: 300 CFM and 67.4 db(A) - This is a new high flow rate model from Ryobi.
So, as can be seen in the specific examples above, battery and corded electric blowers are actually louder than a two-cycle engine gas blower. Of course, there are quieter electric blowers than those shown above, but they are wimpy sweeper units that are incapable of doing serious leaf blowing.
A-weighting is simply not suitable for making this kind of comparison for a variety of reasons that you can read for yourself on the Wikipedia page that describes it. The best way to assess the noise is to listen to them in a normal use scenario and see what YOU think they sound like. Subjective? Sure. But then, isn't a selection based on noise level subjective already?
I also have one of those Echo PB-250LN and agree that it's noticeably quieter (I'd estimate a highly subjective 10-ish dB) than a similar Stihl blower. If it weren't for the fact that the Echo is a left-handed blower, I'd never have bought the Stihl, which is right-handed. And hard starting. And difficult to keep running. And prone to vapor-lock on really hot days.)
