It is hard to find an ultrawide lens that will work well with both crop bodies and full frame cameras. This is due to the following:

• To get the same angle of view with a 1.5X APS-C crop body one must have a lens with 1/1.5x the focal length of a lens needed for the same angle of view on a FF body.
• For the same focal length, to get a larger image circle needed to cover the full sensor of a FF body, it is much more difficult (and expensive) to design a wide angle lens for a FF body than for an APS-C body.

In general, you'll get the best image quality by using a FF camera with a FF UWA lens like the AF-S Nikkor 12-24mm f/2.8G ED-IF. It will give the same angle of view with your D810 that an 8-16mm DX or FX lens would provide on your D3300. But if you use the 12-24mm DX lens on your D3300, you'll only get the same angle of view as you would with an 18-36mm FX lens on the FF camera.

The reason the FF 14-24mm lens is so much more expensive is two-fold:

• At 14mm it has a wider f/2.8 aperture that requires an entrance pupil with twice the area of a 14mm f/4 lens. This requires lens elements with larger diameters.
• It must project an image circle with a diameter of over 44mm, compared to an APS-C sensor that only requires a 29mm image circle. This requires bending light more strongly at the edges of the wider angle of view.

Keep in mind that if both lenses are 14mm, they will magnify by the same amount in terms of the image they project onto the camera's sensor. To get a larger image circle means the lens with the same focal length must collect light from a much wider angle of view. This requires the FF lens to bend light from the wider angles much more than an APS-C lens has to do for the narrower angle of view it provides to a crop sensor.

To put things another way:

• If you use the 12-24 f/4 DX lens on your D3300 or on your D810 (which will automatically crop to only the center part of the D810 sensor that is the same size as the entire D3300 sensor), you'll get the same angle of view as an 18-36mm full frame FX lens would provide on the D810.
• If you use the 14-24mm f/2.8 FX lens on the D3300, it will give the same angle of view as you'd get with a 21-36mm FX lens on the D810.
• Only if you use the 14-24mm f/2.8 FX lens on the FF D810 will you get the widest angle of view. You'd need a 9.3-16mm lens to get the same angle of view with the D3300.

For astrophotography, you really want a lens with the widest aperture you can afford. You'll usually get much better results using a FF sensor with a 14mm f/2.8 lens than a crop sensor with a 12mm f/4 lens.