It's like being on a moving train, and tossing a rock to your friend within the train car. Everything is moving the same rate, there is no difference.
So directly (from the eastward or westward direct of the throw), there is no difference at all along the equator.
However, there is still one difference in rotation rates for paths at the Equator. As the rock goes UP, it will have less velocity than required at that height (because the horizontal velocity needed to maintain the same rotation rate is more), and so it will lag behind. It will wind up west of where it should have... regardless of whether you threw it east or west. This difference is only a factor of the vertical component of the throw.
That said, if you're throwing it, it's going to be a pretty quick trajectory. Short distances and times have very little Coriolis deflection.
The amount of deflection becomes a nonlinear PDE (as early Coriolis alteration in the path changes both its subsequent landing time and its upcoming Coriolis deflection), so I don't believe you can derive a simple formula for the true percentage change.
But for a typical throw attempting an east or west motion, you won't have much vertical velocity, and gravity is very good at removing that component quickly. The deflection for a typical strong human's throw will be on the order of millimeters or less (this is true wherever you throw it on Earth).
The percentage of horizontal deflection would actually be infinite if thrown straight up (since a millimeter divided by 0 is still a "giant" change), and will quickly become a minuscule percentage if any horizontal component is given to the throw; a footballer's pass will not be noticeably altered by Coriolis anywhere on Earth. Air resistance/wind will be much much more significant factors. Even for missiles, which have much more velocity and so can fly for much longer times and thereby reach areas with significantly different rotational momentum, Coriolis deflection will only be on the order of a small percent. But a few percent can mean a few km/miles for intercontinental trajectories... kind of important for a targeted missile!
Only things that can stay "aloft" "permanently"... i.e. fluids (gases, and also liquids)... does Coriolis have a relatively giant impact (causing air that should otherwise flow directly from high to low pressure into air that rotates along isobars)