If noise is the problem, the difference in light level between a good image and too noisy is very close between full frame and modern Dx. It might mean a difference in being able to shoot closer to sunset by 10 minutes or the difference between 1 and 2 candles on a dining table, or slowing down the shutter a stop. That threshold between usable and not is so close that it is often made up for by a little creativity or realizing lower res cameras can shoot slower for the same perceived blur so reducing shutter speed a stop increases motion blur less than a high res camera with a 1 stop full frame light gathering capability. There is no magic bullet when light is poor. The worst low light images are those shot at higher ISO trying to make it seem fully exposed as daylight. I suspect a lot of people allow very high ISO because they seek a daylight sort of luminosity in a dim scene. The camera is not a nightscope and dim light is not just less bright but also has less color and detail information. Trying to ignore that simple fact that in dim light there IS less detail and less color, it is not just lack of camera sensitivity, there is little detail and color information in the photons. A better image is usually possible in letting the scene be dark, some of the best art in photography is setting the mood and message with deep shadows and, especially in fine art photography. Same with monochrome, use it to good advantage since the scene really has no color when very dim. Trying to bring out color fidelity only makes sense when there is light enough to carry that information. It looks unnatural to our brains if made to look saturated in dim light. Action shots in low light requires high ISO only when the photographer has not become skilled in panning or when trying to freeze something our eye and brain can't. If the subject is still, there is no reason for high ISO noisy images, just lack of understanding of exposure and perception. 1 stop is a pretty narrow range of light conditions for images that can be versus can't be taken. Few photographers can even tell the difference in scene light levels within a stop.
There is little difference between any of these cameras is the broadest range of lighting conditions so I want to caution those with simpler cameras that if you are not getting shots you want to print large and hang on a gallery wall, it has nothing to do with the camera. At this point of development smaller simpler cameras actually, result in more keeper shots due to the key point of being with you. As you climb the ladder of hobby experience and start upgrading, your shot count will go down, for many, go down a lot. The best camera in the world is the one with you so if getting higher end glass, larger bodies, you take them out only when you have the single intent of doing photography. A stroll down to the park is not usually one of those occasions so the much heavier, larger and more valuable kit stays home. Of my advance amateur and pro photog friends, most depend on their smartphone for those casual shots that would have been taken by small body DSLRs and slow light zoom lenses. My GF has not taken her Nikon kit on a trip or even out of the house for 3 years because of the ease of using the camera that is always with her.
There are situations where you really need to get a shot where a top camera might help but those are in conditions so extreme that quality of an image is less important anyway. The effective DR of any DSLR in the Nikon line up is not very different, and wider than any camera 12 years ago. In decent light, a requirement for all high-quality images now or ever, it would take very close inspection and side by side comparisons to reference images from a top camera, to hope to guess which image was shot with which camera.
The order of importance in IQ has camera body pretty low on that scale of contribution to the quality of the image.
The factors that make a big difference are mostly free but require a degree of skill, such as having the ability to envision what an image could look like when viewing a scene, and optimizing point of view. Composition trumps camera every time. As does light/shadows in equal measure, account for 80% of the final image perceived quality and interest.
Sure, go buy more cameras, it is fun to have a new toy but in most cases it slows down development as a photographer since it takes time to learn the device and its traits, whereas a user of their old predictable and well-understood camera is focused more on the elements that make good images; lighting, composition and vision. Those on the constant upgrade cycle only really master their old camera by the time a new model comes out and the learning curve starts anew.
I don't suggest anyone switch to full-frame until their budget allows the glass required, and they can explain why one shot or another would have been better. I find the most common justification for jumping up in hobby cost by orders of magnitude, is simply because they are not happy with their current image quality. The change in format does not help image quality, that comes from learning skills that cost nothing but takes some time and effort to learn. The composition is free, as is vision, and lighting is almost free.
One thing a new camera does provide however is enthusiasm to go play with it so shot count can go up a bit for a week or two.
So move to other cameras if you like but don't be disappointed if image quality does not improve as much as assumed before buying it. IF one is limited in funds, focusing on those freebies will give the biggest improvement in results.
Here is a graph of PDR for D7200, 3300, 500 and D750 in both DX mode(which is what your lenses would require) and full frame if you invest in many thousands for lenses to cover the same focal length you have now in field of view) Not much difference in practical ranges. The lower end of the D500 is useless with a very poor signal to noise ratio so in the photography range, every Nikon camera made can exceed the dynamic range of any display media. Of current cameras, the mighty D5 has much poorer low ISO performance than the entry-level D3300 but that is not a problem either, no one complains about poor DR on the D5 at ISO100. As can be seen, if an image is just too noisy, it is not going to be much better with any camera out there but using different technique has more of an impact now that sensor technology has matured as it has.
