I used to build parabolic antennas back in the day (early 80s) most factory built and home built had a F/D ratio of .32 - .36, for deep dishes, you could purchase a feed horn ring that slipped on the end. or just get a feed with adjustable scaller rings.
Advantages of shallow are, that long focal length allows more space between feedhorns and less loss for those parasitic feeds for not being at the cherry spot. also when building, the antennas were cheaper to build flatter and came out a bit larger.
Deep dishes were often used in areas where there was a lot of TI due to Ma Bell microwave towers using same frequency band. I even saw someone put a 10 footer in an empty pool. not much of an issue now days as telcos are using higher frequencies.
As for the look beamwidth, this is more related to diameter, higher gain means more directional, this goes for all atennas.