Godzilla flippers are more flopped compared to most other sterns. That means their resting positing is a bit lower. It helps to make the far left and right shots easier but it also means it can be harder to trap the ball because their angle is also shallower when in the up position. That may be what you’re feeling and it does take getting used to. Maybe share a pic of your flippers and what pitch your game is at.

Godzilla has a 'sweet spot' in terms of playfield pitch.

The back of the game should be jacked up to where on the playfield you have 6.7 degrees of tilt.

There is an app you can get on your phone to level pinballs.

If you are running at 6 or 6.5 degrees, the balls won't want to nestle when you hold up a flipper.

The more playfield pitch, the more the ball wants to go 'downward' instead of 'mostly downward'.

The reason your experience with new Sterns was that the ball went to the flippers faster and was more easy to catch is because pinballs for money usually have very steep playfield pitch. 7 degrees or higher is common.

If you want more control try using superband rubbers