It is impossible to predict which for these designs will provide the optimum reception in any situation as the reflector efficiency, feed horn illumination and ground noise rejection all come into play.
Yes, and the feed design will also have a fair impact on the on the efficiency, cross-polarization, gain taper, etc. Unfortunately this is not typically well exploited in the FTA domain.
An offset design will out perform a prime focus design of similar efficiency by approximately 10% if both are outfitted with an appropriate feed horn and optimized placement. An offset design performance advantage can be noted during reception of low elevation satellites due to the reduced collection of ground noise by the LNB.
I'm not sure what the 10% refers to. If it's an improvement in CNR, I am a little skeptical as that would translate to nearly a dB of improvement. Any difference that substantial would probably reflect a poor feed/dish mismatch or a mediocre taper.
In terms of the performance of offsets vs. prime-focus on low-elevation satellites, that can be interpreted in more than one way. As an example for a given, moderate latitude location on a polar mount, the performance of an offset in terms of ground noise rejection is actually best at true south (highest-elevation satellites) when the feed is pointing at its highest. As the offset dish is rotated on the polar mount to the low-elevation extremes, an offset feed will lose this advantage. Conversely, a prime-focus feed has the worst ground noise rejection at true south, but as the dish becomes more vertical, there is less ground illuminating the feed. In fact it can make sense to change the gain taper for dishes that spend more time in one regime or the other. I have done this and it is effective.
Most performance gains when comparing reflector types with similar efficiency and gain will be the result of rejection of ground noise.
Perhaps this actually reflects more the quality of the feed match to the dish, which has ground noise rejection as one of its effects.
If the offset design is designed for single satellite collection, an increased ratio of height to width will provide better rejection of terrestrial noise and an increased ratio of width to height will provide better rejection of adjacent satellites.
I will allow that gain tapers/feed illumination patterns are not a step function, so some of what you say here is true. But if we take a reasonably well-matched feed and dish that is not leaking an appreciable amount of ground noise, adding more material to an offset width or height is going to change things very minimally because this additional area is not being illuminated to any significant degree by the feed.
So this leads to a related question about the GeosatPro 1.2m offset dishes you sell. They have a fairly low f/D (0.5) as offset dishes go. This should translate to great ground noise rejection, but at the expense of gain given that many offset feeds are more intended for higher f/Ds. Was this an intentional trade-off, and does it make sense in view of the 'offset advantage'?
I've always been curious about this. Don't get me wrong, I love my GeosatPro 1.2, its performance is excellent and the quality of its build is perfect for the price. I almost don't want to touch it as I can't imagine it doing much better, but my calculations suggest I would do a little better by matching a feed to its f/D.