You may find the low priced USB spectrum analyzers have the same problems as your sampling scope. Some, if not all of them take a wide bandwidth slice, and then digitize it, just like the scope did, to generate the FFT by calculation. It is cheap, but not nearly as good as a real spectrum analyzer that uses actual bandpass filters to discriminate between frequencies.
All quality modern spectrum analyzers use digital IF filters as they are simply far better than any analog filter. Analog filters are used for image frequency rejection and anti-aliasing, not defining the spectral resolution. High end real-time spectrum analyzers digitize a wide band of frequencies and use FFT to generate the whole spectrum at once. There is nothing intrinsically wrong with using an FFT for spectral analysis, and in fact it has many advantages over a traditional approaches both in terms of throughput and accuracy.
The problem with oscilloscope FFT features is primarily the poor software implementation -- mostly due to a lack of DSP resources and memory. The analog front end and ADC is not optimized for a spectrum analyzer appliction, but it is good enough to give a much better result than what you actually see.
The problem with the cheap USB spectrum analyzers is mostly the lack of a high quality analog front end. They both inject noise into your system and have a lot of spurs and aliases from the front end mixer that are not filtered out as well as in a "real" SA.
Anyway, I have the signal hound unit. It performs OK for my application but there is substantial noise coupled from the USB signals onto the input port (most of the noise only appears during data transfer). Likely it would be better off with a separate power supply rather than being bus powered. It is definitely not a high end unit, but they seem to be fairly honest about the limitations. The software can be a bit slow and unresponsive -- you can't cancel a sweep in the middle, and you can easily accidentally start a 30 second sweep.
The aaronia units look too good to be true on paper, so I assume they are. Even so, I would have gotten one if I could see a review by someone who appeared to know jack all about RF. Unfortunately, I could find no such review. I would love to hear a review of either their high frequency or low frequency analyzers -- especially the low frequency units as there are very few comparable units on the market at any price.