The first one is front focused, your shutter speed of 1/1250 sec was fast enough, it should have been ok.
I'd try to test your lens for accurate AF on a static object about 50 feet away. Use a tripod and take 5 or 6 photos normally, resetting the lens to infinity before each shot.
Then put the camera in live view using live focus, and take another 5 or 6 set the lens to infinity between shots.
If the live focus shots looks sharper, then your camera, or your lens, or both need autofocus Micro adjust.
By doing the tests above, you will know for sure if the focus is accurate. Live focus is always the best possible focus, it uses the contrast of the image under the selected AF point to adjust focus. Its slow, but accurate.