Thought this might be a fun discussion. So I realized that my own personal collect is split 50/50 between games with classic shooter rods and games with push button firing.
I came to this realization after seeing so many cool custom shooter rods that I can't use on my push button ball firing machines. (Mario and WWFRR)
The shooter rod is a classic icon of pinball machines where the push button is more of a special novelty that most machines don't use but it does make it stand out from the rest.
With shooter rods you control the speed of the ball which usually ends up being a skill shot to where you used the right amount of power at the right time.
Most push button games the skill shot is usually made with the flippers hitting the ball somewhere. Whether its a target, ramp, ball through etc. Like hitting Yoshi in Mario. Or you end up picking a mode like in WWF Royal Rumble.
This is just some small examples but which do you prefer?