It shouldn't be disappointing, it is just a characteristic. You have to know the characteristics of your test instruments in order to use and understand them properly. This is what RTFM means!
Some meters have selectable test currents for the diode ranges, but if not, 1mA is somewhat standard. It appears the Brymen uses less for some reason. There is no 'correct' answer and in most applications, the lower test current would be fine.
b/t/w, your 8060A is one of the best handheld DMMs in the history of test equipment, so it will be tough for new ones to "measure up".