Does your cab have a tweeter? Different setups might reveal more. Would you be comfortable blasting that difference through a PA? Quite the opposite of a microscope. I wouldn't be comfortable doing that with the Classic, especially if anything down my signal chain from it might be amplifying the hiss before the PA does.
There's a vast difference in the published specs in the signal to noise between the two, 75 dB vs. 90 dB if I recall correctly. Real world it's a night and day difference between my two units, with treble boosted or not, using batteries to make sure it's not a power supply issue.
I liked the SCR-DI so much that I bought the Classic so as not to have to pack the much larger and heavier SCR-DI around. End result, I'd rather pack the much larger and heavier SCR-DI around to avoid the noise of the Classic.