[Kevin Ainsworth]

We did a catapult in 2014 and this year.

There are two reasons we found that the balls behave differently.
Your issue looks to be #2, but #1 might be contributing also.
Read below for more detailed information.
The new ball doesn't move as far up the cup as the old ball does.
Looks like your old ball slides up further, causing the ball to be further from the catapult fulcrum, causing more height/speed/etc. Sounds like the new balls are shooting lower, which is to be expected. They are not sliding up as far and shot from a slower/lower position on the catapult arm. We have a soft noodle behind the ball, mounted horizontally, and we do not allow the ball to move in relation to the catapult arm during the firing. This results in more consistent shot trajectory. A ball resting in the catapult where a huge chunk is missing can still cause issues, but not much you can do about that.
The higher spring back to the older balls also can add launch force and would add to the issues listed above, but to a lesser amount. The large surface area you have should reduce this effect to a minimal contribution, one benefit to the large cup method of containing the ball.

#1 The ball is "squished" when the catapult is fired and when the catapult comes to a dead stop the ball rebounds (springs) off the catapult. The different balls have different spring rates, for different reasons. Balls with large chunks missing tend to rebound back to their original shape faster since the foam can fill back up with air faster due to the large opening in the skin. Whereas the new balls expand back slower due to the single small vent in the skin requiring time for the air to reenter the ball. The amount of foam added also differs so some are denser than others. This requires you to slow the catapult arm down at the end of its travel to allow the different balls to rebound (return to their original shape) slightly before leaving the catapult. We found that allowing the surgical tubing to have minimal preload when the catapult arm was at firing position, allowed the catapult arm to slow down slightly before the limit straps stopped the catapult arm. This allowed the catapult to decelerate slightly and therefore allowed the ball to start returning to its normal shape before leaving the catapult.

Another cool catapult was 469's catapult from 2014. We were planning on using this type of device until we prototyped and found it was not necessary for the low forces required this year. 469 used a technique for reducing the stopping force distributed into the robot when the catapult reached the end of its travel. We were planning on using it to slow the initial arm speed so the ball moved a minimal amount with our long travel, tall catapult. 469 had an intermediate arm which they pulled on to load the catapult, it was tied to the main catapult arm with surgical tubing that acted as a damper. This allowed the main catapult arm to start off slower due to the rubberband effect. The intermediate arm pulled the catapult arm, and ball, via the surgical tubing. The intermediate arm also kept pulling after the catapult arm hit its stop reducing the force the catapult arm was exposed to and lessening the movement of the robot when the ball was released. Check it out, pretty cool idea. I would love to hear 469's explanation for their 2014 catapult, but that's our take on it.

#2 Depending on your "cup", "flinger", "cradle", etc. the way the ball leaves the catapult is also important. In 2014 we used manually adjustable flinger ramps that allowed us to vary the angle of release slightly to dial in our shot. The large balls would roll up the flinger fingers and the angle of release allowed us to adjust the height/release angle of the shot. That worked in a year when the balls "slide" along the flinger consistently. This year we found retaining the ball for the entire shot gave us more consistency. This years balls are tacky when new and more slippery when worn. So allowing the balls to slide or grab onto elements of the catapult can cause them to move up or down on the catapult arm (cup for you) and mess with the shot trajectory.

Hope this helps.