Thanks for those comments. I am shooting song birds in thick leafed out tree branches right now. I know that is not easy for any lens really but I have everything set to single focus point to try to get on moving birds and avoid leaves. But I am just wondering if something like a D500 or D810 would focus that lens better and quicker than the D3300.
The D500 has been one of the go to bodies for wildlife. It has the advantage of being a crop frame, and thus your 200-500 will effectively be a 300-750mm lens. The down side is that it is now out of production, and has a 20 MP. Neither of those should be a deal breaker, as lots of folks take some very stunning images with their D500. You would have to buy a used one, though. MPB currently has several in stock for a tad over a$1000.
The D810 is a full frame camera, so your 200-500 will only be 200-500. On the up side it has a 36MP sensor, so you will be able to crop a lot more without losing too much detail. Only the D810a bodies are available new, and they are pricey, unless you want a grey market purchase for about $2200. Used, the D810 runs in the mid $800s. If you are looking for new, the D850 is currently on sale for $2200 new. This is an extremely capable camera with a 45.7 MP sensor. I currently shoot with the 200-500 on a full frame 45.7 MP sensor camera and am amazed at how much I can crop and still have a usable image.
Shooting birds in foliage is tricky. Manual focus tweaking is the best way I have found to get a good sharp image under these conditions. Perhaps one of the newer high end Z8s or Z9s does a good job of following birds in focus, but they are rather out of my price range.