Not sure about Minecraft (as far I know you can run it on full with fairly low-mid range components).
However, for BF4 to run at a stable 60fps+ at max settings, you will need a more powerful graphics card. I would expect to see an average of 45-55 fps with that set up on multiplayer, with drops to 30 fps at certain points if you choose to run everything maxed.
If you want a smooth 60fps, I would play BF4 with Ambient Occlusion turned down or off, and either choose to lower Anti-aliasing or visual details down (such as shadows).