They should be the same brightness in regulation, but on a full charge the NG will start in direct drive since the Vin > Vf. You'll probably be over 1000mA at first, and the NG will be noticeably brighter. It may or may not be adviseable depending on Vf, heatsinking, and your concern for lumen maintenance.
The GD will be in regulation from the start, and buck or boost depending on the cell voltage.
The GD is more efficient at 85-93% vs. 80-91%, so given that the NG starts out of regulation and overdrives the emitter, the longest regulated output will be the GD.