By Quartz, you probably mean Core Animation. Quartz is simply the Mac / iPhone 2-D drawing API, where Core Animation handles animation of views and layers.
It is very difficult to use OpenGL for performing custom animations on views, but Core Animation is designed for this purpose. It has been my recommendation to people that if they are thinking about doing 2-D animations, even in games, they should look at Core Animation first and go to OpenGL ES only if Core Animation's performance is unacceptable. Core Animation lets you do a lot with just a little code, and there are now plenty of great references out there on the topic (such as Marcus Zarra and Matt Long's new book).
You may wish to refer to some of these other questions for more:
- iPhone board game: OpenGL ES or CoreGraphics?
- Core Animation or OpenGL for simple iPhone game
- Quartz 2D vs OpenGL ES Learning Curve