So, you're comparing ACR with an embedded JPEG and default rendering in CaptureNX with maximum sharpening set. ACR software will ignore the sharpening setting and use its current default, which, if you haven't changed it, will be a relatively low 25.
I'm not sure why you'd want to do this. It's generally a bad idea to over-sharpen at the capture stage, unless you don't intend to do any post-processing.
If, as you say, you are shooting mainly for web and screen-based applications, your target dimensions will be much smaller than the 36MP provided by the D800, so you will be presumably be re-sampling to smaller dimensions. This is normally where people do the critical sharpening. A large screen image is typically less than 1MP.
Is there any chance we can see a screen capture (at 100%) to see what you're describing?