First test is 1 Gatherer and 1 Dwarf gathering from berry bushes with NO economic upgrades. Both are positioned next to an ox cart so that all they have to do is stand up and their food is deposited.
The Dwarf took 5 minutes 1 second to gather all the food from two bushes.
The Gatherer took 5 minutes 8 seconds to gather all the food from two identical bushes.
Second test was 1 Gatherer and 1 Dwarf gathering food from dead Aurochs, with the ox carts positioned as above. Hunting dogs and Pig Sticker were researched, and both Aurochs had the same amount of food left on the corpse - around 360.
The Dwarf took 4 mins 7 seconds to gather all the food until the corpse disappeared.
The Gatherer took 3 mins 59 seconds to gather all the food until the corpse disappeared.
Third test was 1 Gatherer and 1 Dwarf gathering food from farms, with the 1st farming upgrade and Husbandry researched. both farms were built right next to the TC.
The Dwarf took 3 mins 58 seconds to deliver 5 payloads (150 food) to the TC.
The Gatherer took 3 mins 53 seconds to deliver 5 payloads to the TC.
conclusion - they gather food at the same rate, or virtually the same rates. Obviously the test numbers may not be accurate to the true average to the second, but they are a pretty good representation i think.. so maybe the information in the thread should be changed!
note: there is an important difference however, in that the dwarf seems to take 2 seconds longer to build than the gatherer - 17 seconds compared to 15 seconds. however, I think losing 2 seconds of TC time, especially in classical age and beyond (and archaic if the dwarf-build is good enough) is worth it to save 50 food and spend 60 gold you may not need, considering their actual rates of gathering food are near indistinguishable.
I did not test wood, I assume gatherers are quite a bit better at that.