depth of field - Can we always talk about noise difference between crop and full frame?

Let's say we have two systems:

1) full-frame camera, 80 mm lens at f/2.2

2) APS-C camera, 50 mm lens at f/1.4

The subject is the same, as well as the camera position, focus distance, shutter speed and ISO. And DOF is the same too (because of 80 mm lens and f/2.2 on full-frame). And let's say that we compare two photographs from these system, resized to the same size.

Can we see the difference in the noiseness in this case?