You can't expect much from real-time 3D graphics. The render in Blender is done with ray-tracing, advanced lighting computations and supersampling. You can of course increase the number of samples to have more smooth edges but it will also decrease performance, this is done by changing the min samples value before you create the display system.
Only so much can be done in real time. A raytrace render can take hours, when you have only a fraction of a second quality is going to be lost. I'd suggest editing the texture a bit to make it look softer.
If you're using an nVidia card, go to your nvidia control panel, 3d settings, and then drag the antialiasing bar all the way to the end. If you have one of the latest cards then you should be able to get the edges as smooth as in the render.