For the ADF in each, are these single-pass with two image sensors, or mechanical duplex, or non-duplex? If it's single-pass, it's not at all uncommon for there to be damage to one side and not the other, and the "upper" side would never be used when flatbed scanning.

As cardsqc said, this can be a common problem if there's dirt or optical damage in the paper path, but it's implausible that it would be electronics - in any unit modern enough to be a scanner/copier*, there is unlikely that there are much in the way of "copy electronics" or "scan electronics" to be separate by a wire, and it's even more unlikely for a household all-in-one - there will be one PCB, and mainly just software and a CPU - in one case it scans it into memory and either then prints it, in the other it scans it into memory and then transcodes it to a desktop-PC-friendly format.

It's certainly possible that either the transcoding to printer raster values and/or transcoding to the desktop PC friendly format uses a separate ASIC function (rather than being done by the processor**) such that one could have gone bad but not the other, but it seems unlikely.

Two more likely possibilities, one that you can test for:
1) Does the line show up as pure black if you pull the scan into an image editor? If it's not, it's possible that for photocopying, it's using a pure monochrome scan and whatever the obstruction creating the line If you're scanning in color/greyscale doesn't make the threshold for a a pure black when copying. You can test this by doing a pure monochrome scan.
2) It's also possible that the cleanup algorithms or contrast curves are different for the photocopying. Not much to be done about that.
3) If it's two completely unrelated units, and only on scanning, what are you scanning to? If it's directly to a machine via a Twain or similar driver, maybe try scanning to a network share?

Also, are both up to the latest firmware?

If it's damage or dirty, the only "fix" I can think of that may help is carefully cleaning the paper path, and maybe inspecting for scratches although you'd basically have to replace one or both of the scanning

(* I'm sure someone back in the 90s built something that did direct optical photocopying, but also had a scanner, but it can't have been common.)
(** these days the processors are usually cheap, powerful general purpose processors, but especially on older models a lot of printers stuck to much older microcontrollers for a long time, where you'd have needed ASICs to do the transcoding quickly enough. Processors popular in old laser printers and office all-in-ones include some really interesting architectures that never made it to the desktop, like the i960 and NS32)