Stock pictures on global or texture ?

I worked on contrast applications. For littles pictures, it’s better to use texture than global. For big pictures, is it better to stock it in global or to put it in different parts in texture ?

And I have read that texture is size is 2^16 * 2^15 (for a 2D array) ; if we have 1 byte texel, this size is equal to 2 147 483 648 bytes. So does it mean that texture’s size is equal to global size (because texture is allocated from global ?)