How to achieve pixel perfect curves with Photoshop CS6?

Coming from a mobile development background, I have recently decided to learn how to design for mobile apps. I am not yet decided which tool I should use. I don't hold much knowledge in Illustrator and Photoshop - but am trying to create a screen design using Photoshop.

I was under the impression that version CS6 supported vectors and I could create pixel perfect shapes. As you can see below, one the left hand side is a rectangle in Illustrator and a circle in Photoshop. I am trying to achieve the Illustrator end result in Photoshop.

Is this possible?

I am basically trying to do is a design of a button with that end result.

Thanks