I also wonder why some of you are so obsessed with FFT. What is it good for (in this category)? Many old scopes have it too. Practically useless. At least to what I've seen. You need it often? Get a spectrum analyzer! You need it once a year? Dump the data and use Octave.
As nctnico and iMo mentioned, the recent implementations of the DSO FFT can be quite useful indeed. If you search for the recent R&S FFT implementation videos this performance is impressive. Siglent does a good job, but is slow and lacks some features which would augment its' use (log frequency scale for example). We don't have a Rigol, so can't comment on their implementation other than what we've seen reviewed, which seems to indicate some areas lacking.
Long ago back in the old analog Tek scope days, we would take the vertical channel output from the lab Tek scopes and feed this into an HP SA so we could get the benefit of the scope channel inputs & probes (WB Hi Z and such), and see the Time Domain and Frequency Domain results, now the modern DSO does this for us!! Sure the DSO FFT has nowhere near the Dynamic Range of a proper SA, nor the upper frequency range, but has the benefit of the lower frequency range (SA usually don't drop below ~9KHz), and Time and Frequency Domain viewing.
There are speciality instruments like Signal Analyzers that cover the lower frequency ranges and have good DR, but they are dedicated expensive and bulky instruments. Here, when one employs a modern quality DSO FFT implementation, one appreciates the value and convenience of the DSO implemented FFT.
Sure there's lots of room for improvement, but please don't discount the value of a quality implemented FFT on a modern DSO, similar to discounting/utilizing the Bode function...but that's another discussion.
Wrt to the FFT parameters, this can be confusing when jumping between Time and Frequency Domains since the FFT bridges both, whereas the SA just deals in the Frequency Domain and simpler to visualize. Something that can help folks jumping between these domains is to realize they are "orthogonal or inverse" type domains, meaning that something Narrow in one domain is Wide in the other. For example; a narrow voltage pulse in the TD appears as a wide frequency response in the FD, and a narrow frequency response (sine) in the FD appears as a wide response in the TD (long cycles of sine)*.
So when one thinks of FFT resolution (narrow FD) this implies TD length (long), and the Sample Rate (high for narrow pulses) determines the frequency span (wide).
An interesting function is the Gaussian, which has the same general characteristics in both Time and Frequency Domains meaning the Time and frequency responses have the same shape. This was a reason for using Gaussian Shaped Pulses way back in the early days.
Anyway, these are just some concepts that might help get ones arms around the FFT.
* Here the assumption is the signal is continuous before and after the FFT capture window and leads into Windowing Functions which is another separate complex FFT topic.
Best,