Giana isn't an exact clone. The big thing is power ups; they are cumulative in Giana. The more you get, the more stuff you can do. I'm talking about the Amiga version; not familiar with the C-64 version.

Found a little about it here:

To its credit, the game would seem to have a more complex item system that the game it imitates. In addition to Super Mushroom and Fire Flower substitutes — a spinning orb and a lightning bolt, respectively — the Great Giana Sisters also features a more powerful fireball upgrades, clocks to put enemies to sleep and the like. Perhaps best of all, the spinning orb item doesn't just make Giana bigger, but morphs her hair into a mohawk that she can use to break overhead bricks. Gorgeous.

Also, you can see the power ups in this video: