For the same subject framing, a full-frame camera usually gives shallower depth of field than an APS-C/crop camera because you must change the shooting setup to match the composition.

To fill the frame the same way on full frame, you typically either:

• move closer to the subject, or
• use a longer focal length.

Both of those reduce depth of field and increase background blur.

A longer focal length also means a larger physical aperture diameter at the same f-number, which contributes to stronger blur.

So it’s not simply that the sensor itself magically creates bokeh; it’s that matching the same composition on a larger sensor usually requires choices that produce less depth of field. That’s why your friend’s 5D Mark II appears to blur the background more than your DX camera in similar-looking shots.