Both signals were captured with the same ScopeFun oscilloscope, so the difference is due to AWG outputs. If we compare both signals to an ideal square wave signal, we see some overshoot in the ScopeFun AWG signal and some undershoot in the Tektronix AWG signal.
With every measurement there is always some bandwidth limitation, so for capturing transfer functions it's more important to know what is the response of the signal path without DUT. And because we know this information (we can measure it when AWG is connected directly to oscilloscope), we can use it to get accurate measurements of transfer functions, even if the response of the signal path is not perfectly flat.