These are two techniques with two different natures, so discrepancy between results should be expected in the first place.  EDS analysis itself won't provide the same results in multiple measurements for the same sample unless the sample is homogeneous. Roughly speaking, the closeness of results between the two techniques will depend strongly on sample homogeneity and elements under consideration. EDS can not detect H and He, it poorly detects other elements with Z

These are two techniques with two different natures, so discrepancy between results should be expected in the first place.  EDS analysis itself won't provide the same results in multiple measurements for the same sample unless the sample is homogeneous. Roughly speaking, the closeness of results between the two techniques will depend strongly on sample homogeneity and elements under consideration. EDS can not detect H and He, it poorly detects other elements with Z

since i do not know any details of what you did, i can only speculate.

this is probably due to the hydrogen in your sample which cannot be accurately incorporated in the quantification. in addition to that, correct calibration is also important.

The negative value means that the elemental signal is even lower than the back ground. If you want to get the Quantitative analysis of light element in a small area, you can try EELS analysis. But the result is also depending on the model you selected of the cross-section.

Depending on the correction method (ex: ZAF corrections) of the RAW data from EDS, it may be possible to obtain negative values. The physical meaning for that is, the signal level is below background noise (i.e. continuum X-rays - Brehmsstrahlung). 

As correctly indicated and well-explained by others EDS makes relatively "local" measurements and has some resolution and accuracy limitations. According to Goldstein et. al. even under optimal conditions (that is flat specimen, pure-element standards on-site and matrix corrections available) you will still have 5% deviation for each detectable element, if you perform multiple measurements.

Also note that the energy resolution of a standard EDS system is rougly 130eV; and the carbon peak is situated at about 230eV, which means you CAN detect carbon but quantifying it is not reliable.

Lastly also consider the "contamination" problems which can also lead to errors in quantifying carbon content.

Since you have only C,(N?),O in your specimen you should throw away your “results” and find a more suitable method.

EDS is not a good technique for quantifying light elements in specimens consisting exclusively/mostly of light elements. You can get more or less reliable results only if you have standards which are close to your consisting of light elements specimen in composition (and I doubt you can find any).

Negative value means that that element is absent and its value is used by software during normalization procedure. Why you put non identified element in your calculations? You should first perform thorough qualitative analysis and proceed with quantification only for identified elements. So, it looks like you was unable to detect N.

EDS is used for chemical identification of elements and their concentration. XRD is used to identify spatial arrangements of atoms in crystalline phases.

In EDS, electrons knock out electrons from atoms, producing X-rays of characteristic wavelength. These X-Rays are then detected to identify the element from which they were produced. In XRD, X-rays of known wavelength are used to probe the structure of the material, using the lattice as a diffraction grating.

To perform an EDS you need an electron source. For XRD you need an X-ray source.

If you are looking for chemical composition, concentration gradients, or solute segregation, use EDS.

If you are looking for phase distribution, lattice strain fields or stored defect content, use XRD.

Could anyone help me to figure out why is there a negative value in EDS. I am using Ni and Co. Will there be a interference from the EDS system itself.Can Ni suppress presence of Co.

Ni and Co are not light element, so for sure there must be a peak. I find my EDS shows overlapping of Co over Ni.