Despite my own past reading in this subject I've never opened a forum on this comparison, but it's probably time to do so and should lead to all sorts of points of disagreement, especially in ethics but also (or especially) in canonics. Please remember our forum rules and confine this dscussion to philosophical issues rather than the political issues with which she is commonly identified. it may also be appropriate here to talk about "Libertarianism," but again focusing on its philosophical roots and not on its political implementation.
Years ago I wrote this article at NewEpicurean about Objectivism, but there may be people here on the forum who would like to explore the philosophical (rather than political) aspects of this topic.
Objectivism: The “Worst and Most Dangerous” Philosophy In America – NewEpicurean
Given Rand's emphasis on Aristotle and her in her own writing (to my knowledge) stiffing Epicurus from even any mention, I think there are important philosophical problems in Objectivism that would be worthwhile to discuss.
Feel free to comment here in this thread or open your own thread in this section.