First my Brompton that was a S type superlight 6 speed is highly upgraded, most components have been upgraded including the transmission which is now a 14s Rohloff hub.
For the Birdy, I ave two Birdy, A Pacific Cycles Titanium Birdy and a R&M Touring Birdy with 21degree sport stem, hub dynamo+Supernova lights and rear folding rack. Both have a derailleur transmission.
Even with this transmission, the Birdy is a much more efficient bike, less effort and higher speed. This higher efficiency comes from the frame and from the suspension that allow to ride faster on bad roads.
The front suspension is a huge difference with the Brompton, combined with the Big Apple 50mm wide tires the ride is very fast and comfortable. The rear suspension is better than on the Brompton but the difference isn't that big.
About the gear inch range, the Birdy Touring with its 9-32 cassette has a wider gear inch range (356%) than the Brompton 6 speed (306%) but much less than the Rohloff (526%, which is also available on the Birdy).
The R&M folding rear rack for the Birdy (it automatically folds when the rear swing arm is folded) is fabulous, it allow to carry full size rear pannier of Vaude or Ortlieb, something impossible with the Brompton.
I made some upgrade of my Birdy Touring: I added a Brompton front block adapter from H&H to be able to use Brompton front bags. I have now the choice between the front bag, the rear pannier or both simultaneously.
I change the Marathon Racer tires that I do not like for wider 50x355 Schwalbe Big Apple.
I changed the 52t front chainring for a 50t Garbaruk narrow-wide.
The only drawback of the Birdy is that it is slightly bigger folded than the Brompton. Once used to, the folding is as fast as for the Brompton.
One more thing about the front dynamo hub: the Birdy front hub has a standard 100mm spacing but its disc mounting is specific, on the right side and at a bigger distance from the dropout (closer to the bug center) than a standard disc with as consequence that there is only one type of hub dynamo that fits, the special SP8 for Birdy (there was a special SON XS for Birdy disc but its now discontinued).