For this you need to know first the interaction between your material to that of the selected imaging source (X-rays or electron). In EBSD the electron interaction with your material is very small ~ 20nm, but in XRD it ranges from few micro metres to several micro metres, depending upon the target material (also on your material).
Conclusion: Ebsd is very sensitive to surface, whereas XRD gives a broader picture. Hope you got the reason of difference.
If you do not have any gradient, and your materials conditions are exactly as a few µm deeper (as A.S. Yadav pointed out already) which is only theoretically possible because of preparation artefacts, they could be identical. There are a few papers published where it has been shown. However, you need to take into account that with EBSD you get all pole figures completely whereas with XRD a considerable part is missing which needs to measure more pole figures in order to find a model which reprtesents them in an acceptable way. Moreover, you need to consider the statistics. XRD will "always" have a higher statistical relevance compared to EBSD. On the other hand, EBSD gives you many more information (misorientation, pole figures for minor phases which are below the detection limit of XRD, you really see from where you get the signal whereas XRD is an integrating signal). You also should not forget that during the movement of the sample in the diffractometer XRD always combines information from other areas and depths (illumination and detecetion depends the tube as well as detector position). In other words, the investigation of texture by XRD is also not that simply or easy to interprete. For a reliable information you need to take into accound that you also have some drawbacks. You should never forget the assumptions you make if you do XRD. This - however - also for EBSD so. If you have two phases which deliver a signal which can be indexed by only one phase (e.g. magnetite and wuestite) you will never realize this mistake... This would never happen with XRD since the Bragg angles are totally different.