In my experience of it though (only two workplaces, but not one) it's used for higher level planning, rather than being a 'more advanced agile'. I.e. a SAFe iteration spans some number of sprints greater than one. What are we going to deliver this quarter versus how are we going to break down and monitor progress of the quarter's deliverables week by week. (Don't read that like I like it.)

I think you're confused about the terminology. SAFe doesn't have sprints. Depending on the program planning horizon, several iterations can be grouped together into a larger program increment which typically lasts about a quarter.