Apparent size of subject...Will the image of the subject be the same size across both cameras?
IMO, there are three different answers. Which one is correct depends on what you think "apparent size" means.
If two cameras photograph the same subject, from the same distance, using the same lens, then the actual size (measured in millimeters) of the image on the cameras' sensors will be the same. This will be true regardless of anything that you can say about the sensors.
Is this what you mean by "apparent size?"
If the two cameras have different size sensors (measured in millimeters), then the image of the subject will fall on a smaller fraction of the available sensor area in the camera with the larger sensor. This will be true regardless of the pixel densities of the sensors.
Is this what you mean by "apparent size?"
If the two cameras have sensors with different pixel densities (measured in pixels per mm), then the subject will cover more pixels in the camera with the higher pixel density. This will be true regardless of the size of the sensors.
Is this what you mean by "apparent size?"
If the two cameras have sensors with different resolutions (measured in number of pixels), then see above. Resolution, pixel-density, and sensor size are not all independent variables. If any two are known, then the third one also is known:
size_in_mm x pixels_per_mm == size_in_pixels
If you only know the number of pixels in the two sensors (i.e., if you don't know sensor sizes and you don't know the pixel densities,) Then the question cannot be answered.