I don't think SR780 does anything fancy with x-correlation. Each ADC has about 90dB SNR, which is what you would expect for a good 16-bit DAC. It can calculate cross-correlation between two channels and has many other features, such as swept-sine measurements with a build-in source.
I just looked at QA401, its noise level is about 10 nV/sqrt(Hz) at high frequency, going up to 30 nV/sqrt(Hz) below 100 Hz. Also the bandwidth is limited on high and low end. So it maybe fine for audio work, but for me the spectrum analyzer is useful for general low-frequency low-noise analog electronics development, so it needs to have at least DC-100 kHz (ideally DC-1 MHz) response and as low input 1/f noise as possible.