Ken and Bill, you're not wrong. The problem with this thread is that everyone is talking about different things yet discussing as if they are all the same.
This is going to be lengthy but let's step back and talk about the print making process as a whole system made up of individual, separable components. Ie, we're going to walk through a systems analysis. The system is made up of a lens, camera and photographer, the negative including development, the final print including development, and finally the viewer or instrument examining the final print. Each of these components introduces its own degradation in the transfer of information between original object and the final image.
As a linear system, the transfer of information can be and has been characterized to great detail in many different ways over the centuries. The exact method isn't necessarily important for this discussion, but the key point is that the effect of each of these components can be divided out and analyzed separately to determine what their effect is on the image.
This fact also allows us to assume some level of equivalency in various components to discover the source of differences in quality between the prints generated from different-sized systems (ie camera formats).
So we assume the camera and photographer provide equivalent contribution (mirror slap, shaky hands, etc..essentially vibration and miss-timing of exposure), so when finding the fundamental difference this contribution can be ignored.
That leaves the lens, negative, print and viewer.
The fundamental question assumes the prints are the same size (makes sense), and an unspoken assumption that the viewer also is the same (also makes sense). This leaves us looking at the two true variables:the lens and the film.
There is a difference in how the lens images between the small and large formats. During the discussion I added the point that aberrations scale with a lens. A 50 f/2 and 250 f/2 are scaled equivalents from a design standpoint, in that their aberrations, ray trace, image format and layout all look the same ...but just different linear dimensions proportional to the ratio of their focal lengths. They both provide the exact same image information formed onto their respective image circles. As such, the smallest resolvable spots for the longer lens are larger by the ratio of the focal lengths. This has an impact on the MTF. That I showed with the plots I posted, although some would still argue the sky is green. So by virtue of this scaling, the smaller lens is capable of transferring much higher spatial frequencies (fancy way of saying better resolution). but we'll see for this comparison the ability is negated because we want to look at images of the same size:
Ignoring for the moment the effect of the film and print components of the imaging system, if you were to take the image formed by the lenses and make them the same size, they would look the same. Those 200 lp/mm (for example) that the smaller lens recorded has just been resized to the same 40 lp/mm of our larger lens. There's a caveat to that thought exercise: assume the lenses are not near diffraction limit. Diffraction is a function of wavelength and f/#. For the values above (f/2) we're probably nowhere near diffraction limit. However, if we stop the lenses down, then at some point the formed, resized image (remember we're ignoring the film and print effect for now) will look different and the nod goes to the larger lens.
But let's keep the lenses at an equivalent, wide open aperture setting so we can look at the effect of the film by itself. This one's pretty much a no-brainer I think. The image recorded by the smaller format negative, when enlarged to the same size as the larger format negative, will show a different image due to the recording ability of the film grain itself. Again, the advantage will go to the larger format.
Let's release the theoretical limits and discuss real systems: for larger formats a design is never simply scaled up. Weight and size considerations means larger lenses are typically different (though similar) designs at slower f/#'s. This is where maintaining the same DOF comes into play, but muddies the waters when trying to examine what each system variable contributes. These changes all improve the capability of the LF lenses to produce a print which, when compared to the enlargement from the smaller negative provides a sharper print.
However, giving credit where credit is due, the optimal f/# setting on a good 35mm lens with very fine grain film does have the capability to provide a print as sharp as one generated from a large format camera. One other very practical point to consider, when the very real constraints of size and weight are incorporated into the design, I've found that smaller format lens are much more capable of higher performance at a given stop than a larger format lens (this isn't limited to cameras using film as the media). Weight and size requirements always trade off against performance. In other words, I can do a heck of a lot more with a pound of glass at 35mm than a pound of glass at 8x10.
So nobody's wrong, we're just talking different aspects of the system as a whole, or worse, changing more than one thing about the system at a time without first establishing what each component contributes. In fact, it seems we're all in violent agreement, coming to similar conclusions based from our own individual experience. Ie beating a dead horse.
