Can someone tell me which is more efficient -- Gimp, or Inkscape? I am new to linux.
Check out this wonderful explanation for the differences between vector graphics and raster graphics.
If you want to work with photographs (raster images), GIMP is your best bet. There are lots of brush and plugin collections floating around the net, too (e.g. see here).
If you want to create logos, diagrams and illustrations (vector images), use Inkscape.
GIMP is a raster/bitmap graphics editor software. These software are used to edit photographs and graphics, add effects, make them stylish, etc. Its equivalents are Corel PhotoPaint and Adobe Photoshop.
Inkscape (and others like Xara, SK1, Skencil, etc.) is a vector graphics editor software. These are used for more artistic, precise, and mathematical graphics designing. (See? Designing, not manipulating.)
Vector editors are based on the concept of curves and dots, etc. when representing an image (thus such images too are called vector graphics). You can stretch them but there'll be less loss of quality, as these software are heavy and perform mathematical operations to calculate and re-calculate image attributes. However, these lack specialised photograph manipulations and can rarely make a scratch on, say, photographs, hand drawings, etc.
Raster/bitmap ones produce (called export) 'images' only, in the formats like .jpg, .bmp, .png, etc. unlike .pdf or .cdr. These software have the power of making lots of edits to images or enhance pictures in many ways.
In a graphic editor's system, both are a must (that's why Corel gives its Graphics Suite with both kind of editors). However, Inkscape will be more usable if your focus is precise networking-style graphics designing with formulated and layered mechanisms. If you need a software that will handle image manipulations beautifully, go with GIMP.