I know that FX format cameras have a wider angle of view because of it's sensor . And I also know that noise problem is much more less ( or none ) than that of DX format cameras because of its high ISO range . I want to learn that ; Do FX format cameras have much higher image quality than that of DX . ( sharpness, colors, contrast etc. assuming the same lens will be used in both cameras )
The primary advantage of FX bodies over DX bodies is as you note better high ISO performance. FX bodies tend to have slightly more Dynamic Range and Color bit depth as well, though the differences are small and there are DX bodies that outperform some FX bodies. FX bodies have about a 1-stop narrower DOF than DX bodies at the same Aperture setting.
>Do FX format cameras have much higher image quality than that of >DX .
No! With regard to sharpness, colors, contrast, etc.... the difference between FX and DX is negligible.
There is no general answer to that question, because image quality depends on a variety of factors.
Noise and dynamic range depend mostly on the size of each photosite (pixel) and the new-ness of the camera's processing engine. A camera with larger photosites will tend to show less noise than one with smaller photosites. The theory that "FX is better for noise" relies on the fact that many FX cameras have larger photosites than DX cameras - but that's not universal. Similarly, a newer camera design will tend to be better than an older one, given the same photosite size.
As Marty says, the only aspect that is clearly different with FX is Depth of Field - because it is related to the physical size of the sensor.
So, it's really impossible to generalise about this - tell us which DX and which FX cameras you're thinking about, and then we can answer the question
Regarding angle of view, what you say is correct but really needs the rider "...when the same focal length is used".
I wouldn't do it for that reason. Today's DX sensors are quite good, including the one on the D7100. What attracted me to FX (and still keeps me there for most of my shooting) is the larger viewfinder image, the better low-light performance, and what I believe are generally better lens options.
Your D7100 is more than capable of delivering outstanding Image Quality. Unless you are shooting sports in a dark gym or night field sports under the lights, and a few other situations, it will be extremely difficult to see any difference in IQ between an image captured with a DX body and one captured with an FX body.
I have a DX (D300) and a FX camera (D 4). As Brian says there is no main answer. The DX camera shoots pretty fine pictures and the FX camera shoots pretty fine pictures. The reason I use the FX camera more is higher ISO (I can get the shoot) and faster picture frame (I can get the shoot). Apart of that no one would see if a picture was shoot with a DX or FX camera.
One non-analytical, or non-mechanistic way to get at image quality is to simply shoot the same image with DX and FX bodies. When I tried that (not a double-blinded test so maybe there was some confirmation bias) the FX images "just looked better." I used a D610 body and the 24-85 kit lens (which is a high quality lens but not stellar).
That was in full sun with no motion, and the difference was substantial. I could not say what it was about the difference either.
A friend tried the same thing and also abandoned DX. He is way more into photography than I am (twin D810 bodies; takes photo expeditions all over the world, etc.).
So I'd say try an FX body -- rent one. Have 1-2 friends help with a double blind test. Shoot a variety of subjects. See what you think.
But most importantly, upgrade your mid-range to telephoto lenses even before you do a test. A good lens will be a 10 or more year investment. A body will be superseded every 3 years or so, until we hit some sort of "good enough" limit. Maybe the D8x0 series already has...
>I have a D7100 and asking to myself if I should change it with an Fx body to get high quality superb images.
I went through the same thing with my D7100, thinking I could get better images, specifically portraits, if I only had an FX camera. I had bought some good lenses, so it must be the camera holding me back. I took some classes through my local camera store and found out the camera is more than capable, it was my limitations keeping the images from being as good as possible.
I'm still learning, but my money is going more toward education than equipment... now that I know better.