yeah the basic content pipeline is compatible across a wide range of software, so you can create stuff in z-brush, 3dsmax, maya or even bryce and export it as fbx to unity or UDK... these are the softwares covered by the "art /design" approach... you'll get a tremendous advantage if you do BTech or BE which are the prerequisites for gaming courses (ICAT in Chennai offers these I blv) that dont restrict you to existing technology and teach you to design games from the ground up - as in making a racing game in C++ as against making a racing game using 3DSMax+Unity which is much much easier
so after 12th its anytime better to do BTECH/BE as against a game art/design course
seriously, the art/design approach is very flimsy atm, one basic example is that most animation content in ad films/ movies use 4 sided polygons - quads for modelling, but every game engine will use only triangles - 3 sided polygons for modelling, this basic distinction is not made in the modules covering modelling, so you will be taught to model 4 sided polygons only - so although the courses may be called "game design" they are actually "3d animation" courses adapted to game design
so after 12th its anytime better to do BTECH/BE as against a game art/design course
seriously, the art/design approach is very flimsy atm, one basic example is that most animation content in ad films/ movies use 4 sided polygons - quads for modelling, but every game engine will use only triangles - 3 sided polygons for modelling, this basic distinction is not made in the modules covering modelling, so you will be taught to model 4 sided polygons only - so although the courses may be called "game design" they are actually "3d animation" courses adapted to game design