Ok. I was searching for comments on difference in 0.050 and 0.063 chain and found this thread. It appears that there were some unanswered questions regarding weight and bar thickness. Here is some data I collected.
Chain#1 72 link, 3/8, 0.063, RS (sharpened once by file), weight = 365g
Chain#2 72 link, 3/8, 0.050, RS (never sharpened), Weight = 359g.
As you can see, the weight difference is insignificant (1.7% to be exact). I don't believe this difference would be measurable in chain acceleration as the chain/bar friction would be much more of a factor IMO.
I also measured two bars I use, one an E and the other an ES.
Bar#1 20" Rollomatic ES #3003 000 9421, 0.063
Overall bar thickness = 0.175"
Weight = 1235g (2lb - 11.6oz)
Bar#2 20" Rollomatic E #3003 000 8921, 0.050
Overall bar thickness = 0.175"
Weight = 1063g (2lb - 5.4 oz)
I guess we are not comparing apples to apples here, but it is worth pointing out that the ES bars are quite a bit heavier, 16% by weight in this case. One last point, I use these bars on an 034 and I can tell the difference in the balance/center of gravity with the ES vs. the E. Running the ES bar the saw gets ever so slightly nose heavy.