The 8903B has a fully analog signal generator and analyzer. On mine, the residual (output loopback to input) is about 0.0020% or less (80 kHz low pass). I believe that the Keithley 2015 is digital/DSP based. Its residual distortion is quite a bit higher, but it does other interesting things like showing you the amplitude of individual harmonics. The 8903B won't do that, but you can connect its notch filter output to a scope to visualize the distortion signal and to run a FFT on it.
A limitation of a digital based system, including a soundcard + software, is the upper frequency limit. You can easily do accurate distortion measurements at 1 kHz, since the harmonics will be in the audio band. But what about distortion at a 20 kHz fundamental? With a 192 kHz soundcard, the bandwidth is 90 kHz or less, so you will only get three harmonics (40, 60, 80 kHz) in your measurements. The 8903B has a measurement bandwidth of 750 kHz, and can generate and analyze with a fundamental up to 100 kHz.