After playing around with the D610 for a few days, here are my thoughts on upgrading to a full frame:
You hear photographers talk about the benefits of a full frame constantly: better low light performance, better lenses, better autofocus, and higher image quality. While I've found these things to be true, I haven't seen as big of an improvement as I thought I would see.
The new controls on my D610 are less intuitive. I typically shoot in manual mode and I expect easy to access controls for shutter speed, aperture, and ISO. With the Nikon D3300, an entry level camera, I had all of this. You could make every adjustment while looking through the viewfinder.
The D610 requires me to take the camera away from my face and hit an ISO button to adjust sensitivity. It's a mild inconvenience, but important when you're in fast-paced situations. Maybe there's an easier way to do things? Let me know.
There's also a really convenient LCD screen on top, but it lacks the one thing it should have, an exposure meter. There's no setting to have the info screen come on after partially pressing the shutter either. That's how I metered with my D3300. Now I have to press a button on the body or look through the viewfinder to do it. I even feel like the auto white balance is worse on this camera than on the D3300. It's no big deal and I can fix the images after the shoot, but why should I? The screen is more contrasty, which took some getting used to.
I know the controls feel a little clunky now, but I'm sure I'll learn them soon. The real reason you buy a full-frame camera is for the image quality and depth of field. It is true that I can take better pictures now, yet the differences are hardly noticeable and you'd never see them looking at a facebook compressed image. Can you tell a difference between my newer pictures and the older ones?
On the plus side, the autofocus is faster and the viewfinder is bigger and clearer. It's wonderful to handle and shoot with. I won't be going back to my D3300 except as a backup. It's the photographer that makes the image, not the camera.
As you can see, high quality images can come out of either camera:
It would be hard to tell which camera took which shot, in that situation. For daytime landscape photography, there's almost no difference. That isn't to say I wasted my money. During heat of the moment shooting, the D610 performs better and has far greater flexibility in post. Full frame also has a certain "look" to it that crop sensors can't match.
In conclusion, if you're new to photography and lack funds, don't assume a bigger camera will make you a better photographer. Finding the right light, the right subjects, and learning a photo editor will do that. Spend your money on lenses and lighting first.