Signal Strength, as shown on the receivers meter, is a measure of the LNBF operation.
Dish size will have no effect.
Signal Quality, the measure of the signal from the satellite, will be enhanced with a bigger dish.
60cm is at the 'theoretical' limits of 'what will work'. Low gain and a great possibility of adjacent satellite interference. Some experimentation may be needed to see if it works for your purpose. Some have used 'small' dishes for particular sat/transponders but not for general usage.
I run a couple of .75 meter Channel Masters*. They are good dishes, but still suffer performance wise than larger. Adjacent interference and lower gain. Although with diligent aiming work fairly well.
*Commercial quality build. Probably perform better than a consumer 'build' dish of the same size. Even better performance could be had with a TX rated dish, IMHO.
If these are dishes you already have or can pick up for free, the bigger one will work better of the two. If you're looking to buy a dish, I'd spend a little more and go with a 90 cm, the performance will be much better and worth it.