The quality of the sensor is more important than the buttons and whiz-bang gadgets. If you shoot in RAW (Nikon = NEF, Canon = CR2, etc.) then only the White Balance and possibly a very small number of other settings will affect the data in the file, aka the "negative".
The D810 has a full-frame sensor and your D3100 has a cropped sensor. Full-frame (aka FX) just means that its sensor compares in size to a standard 35mm film negative, which is approximately 35mm x 24mm. The cropped sensor (aka DX) is approximately 24mm x 16mm. That comes to a crop factor of 1.5 on each side, so the FX has an area that is 2.25 times larger. (For the math-challenged, that's 1.5 x 1.5, or 1.5 squared.)
If you need large "photo buckets" (aka photon capture sites) then FX is your better choice. If you need higher resolution, then DX will get more pixels on the subject.
Both of my Nikon bodies are DX and I use almost exclusively FX lenses. Some say that I'm paying too much for good glass and then throwing away the outer portions. I say that I'm paying for good glass and using the best part it has to offer, while not even recording the edges where all lenses struggle to do well.
I do, indeed, plan to keep my FX lenses for as long as I can! The glass is more important than the body behind it. I just ordered a Nikon 24-120mm f/4.0 as a "lesser" walk-around lens for those times when I'm hiking or exploring and don't want to carry everything. It has the focal range that I want, has the speed of f/4.0 for low light, and it is an FX lens.
I had a D600, which is an FX body. I sold it to get my D500, which is a DX body. I kept my D7000, which is also DX. I plan to buy another D500 and sell my D7000 as soon as one becomes available. This will allow me to have 2 bodies that are identical, making it easier to shoot 2 cameras of the same night sky, or have a long lens on one while the other has a wide-angle lens But I digress...
I chose to have only DX bodies after shooting the same night sky with 2 cameras on a single remote shutter release. The resolution in the D600 was so much less than the D7000, and yet it has more MP and is overall a better camera body. What convinced me was the pinpricks of light from the D7000 compared to the blobs of light from the D600.
Both of them are great cameras, but my comment about FX and DX was not about being able to print large pictures or billboards, it was about resolution, and more specifically about the actual number of pixels that were exposed to the same portion of the image, which was all of those tiny little stars. By my calculation, in order to expose as many pixels as a DX sensor, the FX sensor would need to have about 5 times as many MP as the DX sensor. (I get that by multiplying 2.25 x 2.25, or 5.0625.)
The pixel pitch on a DX sensor means that they are smaller, but the same size pixels on an FX sensor would be only 2.25 times as many, not 5 times. The extra resolution of the DX happens when it takes the center of the image from the lens, which optically magnifies it by another 2.25 times. That is like having a focal length that is 1.5 times what the DX is using. Or it would need to have 2.25 times as many pixels.
In my example, my DX was using a 10-20mm lens set at 10mm, and my FX was using a 14-24mm set at 14mm. Each was on its own tripod and aimed at the same portion of the sky. The DX exposed more pixels of the same stars as the FX.
I'm not saying that DX is the right choice for everyone. I'm simply sharing that one needs to know the subject they're shooting in order to have the right tool for the job.
FX: D600 = 24.3MP (sold)
DX: D500 = 20.9MP (keeper!)
DX: D7000 = 16.2MP (until I get another D500)