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Coming to the D800e from the 5D3. Honestly, on both cameras ISO 3200 is too noisy to print that large. You can't make a judgment about noise from a web sized image. You are simply running into the limits of the sensor. Heck, last winter shooting the D3S (noise king) in ideal (cold) conditions, I won't print those files larger than 16x24. They just simply don't hold up larger than that.
Here are your options:
Apply ample noise reduction. Best I've seen is actually in LR 4 and ACR 6/7. But it's a trade off... Apply a lot of reduction and you clean up the noise but you lose a lot of detail. It's a balancing act for sure.
You can also just accept some noise and not get too close to the print. I'd go much lighter on the Luminance Noise Reduction and heavier on Color Noise. I like the D800 noise MUCH better than the Canon. It looks like old film grain.
You can experiment with stacking images with a program like DSS. That allows you to shoot at a lower ISO and combine the images to create brighter stars. However, your FG will get blurred and weird, so you will need to blend sky and ground images.
You can buy an astro tracking device that will allow longer exposures without star trails. Same issues with the FG.
Don't worry. If you are doing dark frame subtraction, you are getting the best out of the camera. I personally won't print anything 20x30 at ISO over 1600.