It’s not the amount of current, per se, but the evenness of the output impedance. I.e. can it deliver the right amount of current to maintain the correct voltage. The DS and the TSS have a constant output impedance (about 120 Ohms) from sub 4Hz to way past the audio band. The problems that people are having when trying to not use a preamp aren’t related to current delivery, they are due to voltage gain matching and (to a lesser extent) effects of unexpected ultrasonics in some amps.
For gain matching the TSS has the “standard” 2VRMS output for unbalanced and 4VRMS for balanced outputs. It also has 3 attenuators (-10dB, -20dB and -30dB) and the ability to add 6dB to the unbalanced output. Also the ultrasonic noise is lower than the DS and the FPGA has the ability to lower it further.