I cannot testify on the R&S, or,modern FFT SA.
A TG is not a,good test, instead use a single tone, with any traditional swept /LO/mixer/IF analog SA, eg Tektronix 7L5, 7L12, 7L13 or HP 4195A, HP8558B, etc.
change sweep speed with no video,filter observations of shape of tone displayed and level at center.
As,sweep speed is increased, at some,point level at peak decreases and shape is distorted and asymmetrical
The relationship between sweep speed, RBW, sweeping width of a SA is very well documented
See the already mentioned Tektronix Circuits Concept book Spectrum Analyzers.
In Signal processing, the same limitations must apply to FFT Analyzers.
With Kind Regards
Jon