So that's the advantage of using a larger format.
Technically you have 2(or three, or more) cameras in one .. as the pixel density is the same and the lens is the same, you have a wider FOV coverage with the larger sensor camera.
So, instead of needing more lenses to effect the same FOV, you then get by with only the one lens and the one camera.
eg. with the APS-C (or even smaller sensored camera) you have a given restricted FOV with any one lens attached.
Remember that the pixel density is fixed for all cameras sensors, so in effect, the APS-C camera is now limited to a tighter FOV than the larger sensor camera.
If you crop the 135 format sensor to the same FOV as the APS-C camera you lose nothing at all.. ie. the larger framed camera is both types of cameras in this scenario.
For a very short time Nikon had the D800 twins and the D7000 both having the same pixel density, and hence as your question asks.
The problem with determining if there was any advantage of noise in image and suchlike from the larger sensor camera, the issue there was that the sensor tech was askew, in that the D7000 was much older tech.
I can't think of any cameras/brands that have simply scaled up their sensor tech to eliminate that anomaly from the equation.
So to think of how this is an advantage:
Think cropped camera of some type(with the same pixel density as the larger one).
The (supposed) advantage of the smaller format camera is it's smaller size.
The advantage of the larger sensored camera is that for whatever focal length lens is fitted to the smaller format camera, the larger one also uses that same lens.
But the disadvantage to the smaller sensor camera is that if you want a wider FOV capture, you need to not only swap out lenses but you also have to carry those other lenses too(which the larger sensor camera doesn't then require!
The idea that there is a size advantage is not what it initially seems to be .... not to mention the most likely probability that in the time it takes to change the lens, the shot is almost certainly missed.