I've had both in the past.
As has been said they share the same action.
The Falcon has an all plastic handle and the Centre has an angle adjustable anatomical grip and is in my opinion far, far better.
If I recall correctly the rear sight on the Centre is better too.
The trigger is adjustable after a fashion, but I think it's only a sear interlock adjustment and it's easy to over-adjust them so that they go off on their own and damage the sears.
The Centre was sold as an entry level paper puncher and it is very accurate in the right hands - I wouldn't hesitate to buy if you can find one.

The Chinese one is a curio, usual issues - wobbly sights, low power and an awful, horrible trigger (the one I had was at least).