Can complex FFT be more robust to noise than two real FFTs of same complex signal?

[Terminator3]

Assume we have complex signal with noise. I have doubts that complex FFT can be more robust to noise than two identical real FFTs. Although we can perform some operations on both complex and 2xreal FFT result to obtain equal result, we must note, that preliminary result encode noise differently, and following operations can give not equal results.

If we do separate real FFTs of each channel, then result noise of each channel is encoded in separate complex spectrums.

But if we do one complex FFT of two channels, then result noise is encoded in result complex spectrum. Although noise did not become "smaller", i have doubt that as two channels noise and signal encoded in single spectrum, it can somehow influence total encoded noise.

So maybe it matters where noise is combined, inside complex FFT or in result spectrum operation of two real FFTs. Maybe some analogy with compression algorithms, there is a different algorithms that can produce output with similar entropy, but different structure.

Any ideas?

Thanks for reading!