How to compare two DEMs and show their difference?

You could start by getting the difference of the two DEMs. QGIS has a raster calculator tool that should come in handy. Just get tiles of both DEMs that cover the same area and subtract the values of one DEM from the other. That should get you a nice raster layer that shows the differences in elevation between the two DEMs.

Let's say Raster1 is the correct, And Raster2 is the one you suspect it has faults.

They also both are in the same units (since you say both rasters are DEMs the z value should be in meters - I assume we're correct and we compare same things)

You can use rast calc from either package (qgis, grass, saga) to compare them eg:

deviation_rast  = abs( (raster1 - raster2) / raster1 * 100 ) 

each cell from the resulting raster will display the percentage which raster2 deviates from raster1.

After that you can reclassify deviation_rast based on your needs: eg

red -> deviation_rast_value > 75
orange -> deviation_rast_value > 50
yellow ->  deviation_rast_value > 25
green -> deviation_rast_value  > 0

to identify problematic areas - and to choose if you want to intervene or not