3/4 inch or 1/2 inch for vertical pipes.

I am going to run 3/4 copper for my horizontals and was wondering if there is any advantage to doing 3/4 for the verticals? I want a powerful shower and even though the shower vavle openings look kinda small, I thought maybe 3/4 inch would be better than 1/2 inch for the supplies and head?

The only time you might need 3/4" is if you have more than one shower head outlet. "Standard" new showerheads are flow restricted, and 1/2" is plenty. Having 3/4" is almost a necessity if you have more than one. It also helps to fill the tub faster, if your valve is designed for 3/4" inputs (some are, most aren't). It depends on how many outlets are open at the same time. If you have many on a 1/2" supply, you may not be able to maintain pressure - then 3/4" (or even larger!) may be necessary.

Not a pro...

Pipe Sizes

If you're referring to the water supply piping in the bathroom wall and you're installing a regular shower valve with one 2.5 gallon per minute head, 1/2" feed lines for the faucet are adequate, especially if the inlets to the valve are 1/2".
Now if you are talking about horizontal lines in the basement and asking which size piping to bring up (vertically) to the bathroom, it would be 3/4". I always pipe 3/4" copper feed lines to the second to last fixture.

Showerheads

Much of what is considered power from a shower comes from the quality of the shower head. It's design to incorporate air into the water gives the feeling of force or power. An $80.00 shower head is worth as much as the valve.