As you asking I am telling CAT score is a mandatory requirement for admission into the Indian Institutes of Management and affiliate b-schools/universities in India, and GRE score is accepted by thousands of graduate and business schools across the abroad :

In other language main difference between GRE and CAT exam is that GRE exam is for doing Higher studies after Engineering foreign countries like US and UK.. and CAT exam is for doing MBA in some of the top colleges in India


GRE exam info :

Type Computer-based or paper-based standardized test.
Developer / administrator Educational Testing Service
Knowledge / skills tested Analytical writing, quantitative reasoning and verbal reasoning.
Purpose Admissions to masters and doctoral degree programs in various universities.
Year started 1949
Duration About 3 hours and 45 minutes (includes 1-minute breaks after each section and a 10-minute break after third section).
Score / grade range Analytical writing: 0.0 to 6.0 (in 0.5 point increments),
Verbal reasoning: 130 to 170 (in 1 point increments),
Quantitative reasoning: 130 to 170 (in 1 point increments).
Score / grade validity 5 years
Offered
Computer-based test: Multiple times a year (depends on availability of the test center).
Paper-based test: Up to 3 times a year in October, November and February.
Restrictions on attempts
Computer-based test: Can be taken only once after 21 days from the day of exam in every year. (Applies even if candidate cancels scores on a test taken previously.)
Paper-based test: Can be taken as often as it is offered.
Countries / regions
About 700 test centers in more than 160 countries.
(Paper-based test offered only in areas where computer-based testing is not available.)
Languages English
Annual no. of test takers Over 655,000 in 2012
Prerequisites / eligibility criteria No official prerequisite. Intended for bachelors degree graduates and undergraduate students who are about to graduate. Fluency in English assumed.
Fee
US$ 205
(Limited offers of "Fee Reduction Program" for U.S. citizens or resident aliens who demonstrate financial need, and for national programs in USA that work with underrepresented groups.)
Scores / grades used by Most graduate schools in USA, and some in other countries.

CAT exam info :

Type Computer-based standardized test.
Developer / administrator Jointly conducted by the IIMs. Technical support is provided by TCS.
Knowledge / skills tested Quantitative Aptitude, Data Interpretation, Data Sufficiency, Verbal Ability, Reading Comprehension, Logical Reasoning, and Analytical Reasoning.
Purpose Admission to post-graduate management programs (MBA, etc.) in IIMs and various other Indian universities and colleges.
Year started 1950
Duration 3 hours.
Score / grade range 0-450
Score / grade validity 1 year
Offered Once a year (usually in November).
Countries / regions 354 centres in 99 cities and towns all over India.
Languages English
Annual no. of test takers 173,738 in 2013
Prerequisites / eligibility criteria Bachelor's degree (or equivalent) with at least 50 % marks or equivalent GPA (45 % in case of SC, ST, PWD candidates). Final year undergraduate students also eligible.
Fee Rs1600 (US$24) for general category candidates.
Rs800 (US$12) for SC / ST / DA (PWD) category candidates.
Scores / grades used by Various business schools in India