I think I can speak from the point of view as both a photographer, and a designer: not like the general public's idea of drawing pretty pictures, or caring about appearance only, but one who was into ergonomics (not merely anthropometry) and especially cognitive ergonomics.
Getting back to the original question, it is essentially this: does the choice of camera affect the resultant photograph?
Previous posters stated that some cameras might be technically better than others, as in having the film held flatter, etc. However, this is not a valid variable in the context of our investigation. Another aspect is the issue regarding the inherent design and function of the camera, which of course have an effect. For instance, for action photography requiring high-speed shutter, a camera with a maximum shutter speed of 1/100s will not get you very far. If you want to do raid sequence photography, a camera requiring red-window winding would not be good either. If you want to do wildlife photography requiring a very long lens, a camera without interchangeable lens would not help as well.
What we need to see is that, with all things being equal, the choice of camera indeed has an effect on the photograph, by affecting the photographer, in terms of his thinking process in both conscious and subconscious terms.
First of all, the camera is a tool which enables the photographer to capture the image, but at the same time the control of the camera is also an interface between the actual functioning of the camera as a machine, and the photographer's vision.
In the sense of cognitive egonomics, the photographer has to build up a mental mapping of how his manipulations of the camera controls result in the actual mechanical (here we also include electrical/electronic) function of the camera. At the same time the mechanics of the camera also needs to give him the feedback, which is part of this mapping, that it is indeed done. Say, when taking a picture,a digital camera is totally silent, but many manufacturers incorporate a simulated shutter clicking sound to their cameras, as a form of feedback, saying "a picture has been taken". In a film camera, when you wind the film, you can feel the gears moving along with the slight resistance signifying the film is actually being pulled across the film gate, and the turning of the rewind knob serves as an extra visual feedback. Or if your exposure setting will give over-exposure, the camera will tell you effectively that you need to change your setting.
If a camera is designed in such a way that such mapping is not easy to establish, or it does not give effective feedback to the photographer, both in terms of insuffient feedback or over-the-top feedback, then the design would not be efficient enough for the photographer to take pictures with both ease and control. In this context, the choice of camera does indeed affect the photograph.
Furthermore, assuming the photographer has achieved proper mapping with several cameras, the inherent characteristics of the camera would affect the creative process of the photographer. Consider this example: say if a photographer uses two very similar cameras, such as a Voigtländer Bessa R, and a Bessaflex TM, both with comparable lenses which do not work against the inherent characteristics of the cameras, such as a 50mm standard lens. He would very likely find that the differences between a CRF and SLR put him in different mindsets in his creative process.
Through the viewfinder of the Bessa R, he sees reality itself, always looking sharp as focussing is done with his own eye; the camera basically frames a rectangular slice of reality delineating the slice he would capture when he hits the shutter release button. However, through the Bessaflex finder, what he sees is a pure image formed by the lens on a surrogate film plane, where he is removed from reality itself and think more in terms of the photographic image. That is the reason why many documentary photographers continue to use rangefinder cameras such as the Leica M, for the sense of immediacy they afford, not due to the lens quality or whatever.
I hope this post is not too long and involved but in terms of ergnomics and its effects we have barely scratched the surface.
