The D810 has a bit better viewfinder than the D800 and hundreds of small improvements. Noise is a bit better behaved at high iso than the D800 (which produces streaks in the blue channel at ISO 6400 if underexposed in low K light and color corrected; this artifact is not present on the D810 at least to such a degree). Many of the improvements are to improve chances of high resolution: more consistent AF, less vibration, EFCS, also quiter and more pleasing sound. Then there are smaller things. I think the D810 is the best overall package to date in Nikon DSLRs. However, it is due an update soon (2017 probably).
I don't think the price is going up. This family is very popular and is likely to sell well once again, equipped with the AF from the D5. I guess the price will stay at 3200€ and go down from there, once initial demand is satisfied. Stuff that is not expected to sell is priced high, such as the D5. The D810's successor is likely to sell like hot cakes IMO. A lot of people are waiting for more cross type AF points in a camera of this family.
The D750 is another option, it has better image quality at high ISO than the D810. But: the body is just not right for my hands. Many like it a lot, however. VF is ok, but I'm not sure about MF.