I tend to use whiteboards with a team who are all in the room with me, rather than as an individual (although I'm thinking of installing one in my home office, just to see how useful it would be). The iPad is less useful in this case, although I suppose you could get a big TV screen connected (or apple tv). Also, there are apps specifically designed to take and share photos of physical whiteboards…
The real killer for me is still the lag. Handwriting is just painful, although perhaps simple diagrams are not so bad? It seems to me that an Android tablet could distinguish itself by providing both very low lag with something like the Wacom accuracy. The iPad is unlikely to ever reach the ideal 1 ms lag -- I suspect the retina displays have relatively high response times (but have no evidence).
For the iPad, there is this app[0] that actually makes decent use of AirPlay: you can set the TV viewpoint separately from the iPad. Past that (no app can make eraser nub styli better), the Surface Pro might be worth a look, it packs a digitizer (no idea who's, likely Wacom or N-Trig).
There's a lot of variation in responsiveness between different apps. Have you tried Penultimate? You certainly may be more discerning than I, but I've found it to have almost no lag.
I think I must have very nearly every app of this type in the app store. All have noticeable lag with a jot pro stylus, though some are reasonable when just using a finger -- I guess the lag simply can't be seen in that case.
I find handwriting with my fingers to be a bit unnatural, unfortunately; it tends to break my flow.
That's really too bad. Although I'm happy with Penultimate, it's unfortunate that various sorts of latency rarely seems to be considered for consumer electronics.
The real killer for me is still the lag. Handwriting is just painful, although perhaps simple diagrams are not so bad? It seems to me that an Android tablet could distinguish itself by providing both very low lag with something like the Wacom accuracy. The iPad is unlikely to ever reach the ideal 1 ms lag -- I suspect the retina displays have relatively high response times (but have no evidence).