First of all, my first impression of this whole thread is that it's pretty much calling LNBFs LNBS. An LNB doesn't care what kind of dish it's getting the signal from. If anything, as Radar said, it's the feed that might care, not the LNB. I know it's easier sometimes to just call an LNBF an LNB, but it really isn't accurate in a discussion like this.
If you're talking LNB though, one difference is that consumers like us don't really have much access to any high quality LNBs that are part of an LNBF, whereas the separate LNBs available to BUDs users with feedhorns provides a much wider spectrum of quality.
Despite the discussion of whether the view of the dish is circular or not (for a dish that's taller than wide, yes, it will look circular to an offset feed, but dishes that are wider than tall obviously won't), the main goal, as Radar said, is to get the feed to look at the whole surface of the dish and no more, ie to get the maximum benefit out of the dish without picking up any extraneous noise.
Now, though, the part of this that has always interested me, and I have never really come to grips with it, is the analogy of a satellite dish to a camera or a telescope. Being or having been both a photography and astronomy hobbiest, I was very quick to trying to compare sat dishes with telescopes and cameras, with respect to the telephoto and resolution aspects of long focal lengths, and light gathering benefits of low F/D ratios. However, despite some 24 years of thinking about this, I really cannot find any scientific description of a TVRO dish that supports the analogy to the optical devices.
All the equations I have run across describe the resolution of a sat dish as being related only to the gain, and describe the gain as only being related to the diameter of the dish, not in any way to the focal length or F/D ratio. The only way I can rationalize the issue is to assume that it has to do with the fact that the telephoto/resolution/light gathering aspects of cameras and telescopes all really relate to viewing a field of view with light coming from the entire field, while a sat dish is only looking at a point source, but even that doesn't explain why the performance equations don't include FL or F/D at all, so I'm really having a hard time with this aspect.
I really believe that the main difference in performance between a high F/D dish and a low F/D dish is the rays coming from the extreme edges of a low F/D dish hit the dish at extreme angles, compared to the rays coming from the edges of a high F/D dish come in at a much lower angle. So a high F/D feedhorn is generally more efficient at receiving signal from the entire dish, not just the middle, particularly on Ku. One interesting observation I once made, was once, I didn't realize the several pine trees had grown 10 or 15' since I planted my dish, and were blocking the bottom half of my BUD. I was getting very poor reception on Ku, and couldn't figure out why. I went up on a ladder, and was playing with the aim of the feedhorn, and found that I could double or triple my signal by tilting my feedhorn upward by about 20 or more degrees, basically aiming the feed midway between center and the top of the dish. Since that was where most of my signal was coming from, I improved signal by improving the efficiency of the feed on off angle approach to the feed. Basically, since the bottom half of my dish was blocked, my prime focus dish was really behaving as an offset dish, like the bottom half wasn't even there.
Basically, for Ku, except for the fact that most offset dishes are high F/D and most prime focus dishes are low F/D, there really isn't any difference between an offset dish and a prime focus dish relative to performance, other than the obvious fact that the feedhorn blocks part of the signal on a prime focus dish. But I would really be interested in some scientific explanation as to why the equations for gain and resolution do NOT contain any reference to FL or F/D, when the telescope/camera analogy would seem to suggest that they should. BTW, I've asked this same question a dozen times before on various forums, and have yet to get what I thought was an answer that directly addressed the question.