Going from a cheap generic frame to a Cervelo R3, you may well feel a difference, but it's going to be subtle.

The ride quality may be a bit better in that the R3 is designed to be (hate to use the dread cliche) horizontially rigid, and vertically compliant.

It likely will be stiffer in the front end,which may inspire more confident handling, and it's likely stiffer in the BB, so it may feel a little bit snappier.

It wil be a bit lighter, which will feel nice when you pick it up, and maky make it feel a bit more responive.

It's not going to be any great increase in speed.

Shiny new bikes are fun, but don't expect any quantum leap in perfomance. Personally, I'd ride the bike you have awhile longer, and wear it out before I upgraded, and then make the curent bike the beater bike.