The manual says those are specified in basic machine units, which is most likely bytes, just like in other opengl functions. Have you tried passing zeros for offsets, and the size of your buffer in bytes for the size? It should copy the whole buffer.

For copying FBOs glBlitFramebuffer is provided - see http://www.opengl.org/sdk/docs/man3/xhtml/glBlitFramebuffer.xml.

You could also maybe look at GL_ARB_copy_image - the bad news is that it's a GL4.3 extension and so may not be available on all of your target hardware. Otherwise you may be able to do something with round-tripping through a PBO:

// note - these two PBO binds are intentionally the same buffer object
glBindBuffer (GL_PIXEL_PACK_BUFFER, intermediatePBO);
glBindBuffer (GL_PIXEL_UNPACK_BUFFER, intermediatePBO);

// read from source texture to PBO
glBindTexture (GL_TEXTURE_2D, sourceTexture);
glGetTexImage (GL_TEXTURE_2D, 0, GL_BGRA, GL_UNSIGNED_INT_8_8_8_8_REV, (void *) 0);

// write from PBO to destination texture
glBindTexture (GL_TEXTURE_2D, destTexture);
glTexSubImage2D (GL_TEXTURE_2D, 0, 0, 0, 0, 0, width, height, GL_BGRA, GL_UNSIGNED_INT_8_8_8_8_REV, (void *) 0);

All going well, that should run the copy entirely on the GPU, but does have the downside of requiring intermediate storage and an extra copy.

Are you quite sure that you don't have glBlitFramebuffer? If you're using FBOs then glBlitFramebuffer is part of GL_ARB_framebuffer_object (which from a pevious post it seems certain that you are using) so it would be a driver bug if you didn't have it. If you're using GL_EXT_framebuffer_object then you should also check for GL_EXT_framebuffer_blit and use that if available. In both cases you can specify a filter parameter for dealing with different sizes, if necessary.

Also in both cases, the PBO method would definitely work as that's GL2.1 functionality, and FBOs belong to a higher GL_VERSION. I'd definitely encourage you to double-check your hardware's capabilities as they're almost certain to be higher than you seem to think.