Hii,

CAT is a National level Common Admission Test to get admission in IIM's and Some Business Schools to pursue Post Graduation in Management i,e PGDM/MBA. XAT is also another National level exam Conducted by XLRI Jamshedpur for admission to MBA/PGDM Course. Some Business Schools offers CAT and some other XAT. I suggest you to apply CAT exam because you can get admission in IIM's through CAT but not XAT. If you have written Same exams, and the College accepts both you can apply through only One particular exam Score which is better.