With digital signals, you will basically get the same good picture with a smaller dish as a larger dish. This is because the receiver "fixes" the signal coming in.
However what happens during bad weather is that the signal will get to be so bad, the receiver can't fix the signal anymore. Then the picture starts to break up.
This is shown on the Quality meter. The difference is a better signal will have a higher Quality signal level. And the picture will not break up during cloudy days.
Also look at the specifications for each dish. These are on the dish manufacturer's web site. The thing to look for and compair between the two dishes is "Gain". The higher the gain, the better.
So does the larger dish have a higher gain than the smaller dish?
Is the quality reading higher on your receiver with the larger dish?
Also note that there are other things which can improve the quality signal level. The signals on the coax from the LNB to the receiver are high frequency and using quality coax and connectors can make a difference.
I use blue colored high frequency connectors where there is a split or connection in the cable. These do make a difference.
I use quad shielded coax. I use a coax stripping tool. I cut away the outside foil shield, bend the wires back, then cut away the inside foil shield, then twist on the compression connector and "compress" it with the compression tool. These connectors keep the water out and I think they make a better connection/seal.
I use XL compression F-connectors.
Then I recently bought a very high quality low noise
Invacom SNH-031 Universal Ku LNBF and this improved my quality signal reading.
Then
aiming the dish exactly left/right and up/down to get the highest signal reading.