Try opening the QIF files in Apple's Numbers, via File>Open. What happens when you double-click on the QIF file? Does it want to open in Quicken?
I second the the choice of MoneyDance. It is very stable, mimics a lot of Quicken "style". Check out
QIF Importing with MoneyDance. In the sidebar on that same page are links to possible problems and importing for a Mac from other versions of Quicken.