Birds and wildlife are my main interest to which I am returning after a 2 year detour and I've been working the D800 for this subject more lately. The CH frame rate is a disadvantage for birds in action but it's not that bad. The AF improvements are definitely nice. The problem with the D800 is mainly when you plan to use it as a crutch to avoid getting closer. LOTS of wasted disk space if you don't get the shot you're looking for in camera. It adds up quickly.
But if you can get closer... then the D800 is excellent. The D4 has some advantages in low light and frame rate over the D800 but the D800 can still serve you just fine with some practice and accepting its limitations.