The mentioned siglent function gen has one of the lower THDs for bench signal generators, but there is really no comparison to the performance of a decent sound card.
If you absolutely need every parameter characterized and lots of input protection, you can spend tons of money and get an audio analyzer from AP or Prism Sound or something, but that's several grand and it doesn't sound like you even are considering that level of performance.
Going with a purpose-built oscilloscope also means you lose out on most of the wide dynamic range that a modern sound system has to offer - even high resolution 16 bit converters are notably worse than the industry standard 24 bit ADCs used for audio work, and the extra bandwidth means nothing if you're talking strictly audio levels. Faster sampling rates can help responsiveness for a given FFT, but if your software is smart, you can actually do that without extra samples.
Knowing that, I think a PC based sound card will give you the best performance. Something like the QA401 will give you high performance converters and a good software suite, though it lacks standard sound driver outputs so using regular sound software may be difficult, plus if you need phantom power or audio-specific connectors you are out of luck. The route I went was to get a high quality recording interface that is just standard audio gear, but then you can use almost any PC based software you can find, and there are several good free ones. I like Spectrum Lab and Arta for free tools, but there are many pay options and if you have Lab View or similar mathematical manipulation tools, you can code up whatever analysis and graphing tools you can desire.
Bottom line is that aside from the very highest end audio analyzers, you're going to get the lowest noise and THD from DACs and ADCs designed specifically for audio use in well designed interfaces, and having the flexibility that computer software affords you, you can do a lot with the cleaner signals coming in (FFT size limits be damned when you have several gigabytes of main memory to deal with). It's easy to get a THD+N floor of lower than -100dB for only a couple hundred bucks in a sound card, and getting to even -95dB or so can be quite cheap. On the high end, you can get to -110dB or better for probably only a little over $500.... none of the cheap(ish) 90s era test equipment can really touch that level of noise performance and it's well beyond the dynamic range of human hearing. With older dedicated test equipment you get the built in functionality, input protection, and extra characterization, but you sacrifice the digital hardware limitations (processing power and memory size), the noise floor of modern audio equipment, and the flexibility of using whatever software you want.