The G6 will offer more control, the iPhone is simple to use. A typical web-sized photo usually less than 1 megapixel! A 7 megapixel camera is plenty.
If you're using Instagram from an iPhone then you're basically taking photos of things "as they are" and you're not yet exploiting the camera to control how something appears. As you learn more, you realize that you can use manual exposure controls to freeze action, or imply motion by deliberately blurring action. On a camera with a larger sensor (neither of the two cameras you have can do this) you can adjust the aperture to create an image with a deliberately blurred background and yet still have tack-sharp focus on the intended subject.
You can learn the basics of exposure via a book such as Bryan Peterson's "Understanding Exposure". The book requires that you have a camera that can shoot on "manual" (which your G6 can do) but some of the creative effects work best with a camera that has a large sensor and a lens with a low focal ratio (which the G6 doesn't have). I wouldn't worry too much about what your equipment is... learn the techniques. You'll actually be a much better "shopper" once you realize what features control the exposure... you'll have a much stronger understanding of what sort of camera you'd like to own (and why).
You can learn about composition from Michael Freeman's book "The Photographer's Eye: Composition and Design for Better Digital Photos" -- you can learn about composition and design with ANY camera.