When I visited Vienna a few years ago, Franz Josef seemed to occupy much the same position as Queen Victoria does in Britain. As a ruler he made plenty of mistakes, but his lasting popular reputation is as a benign grandfather figure, neither inept like Nicholas II nor an aggressive blusterer (and even proto-Nazi) like the Kaiser.
Ann
I wonder how much that has to do with just simple longevity, which inevitably softened his image as it did Victoria's? If he'd died or been deposed in middle age, I doubt that his reputation would have survived so well. He also enjoys a certain cult status in the *former* Habsburg lands, as does his wife far more so - who in her lifetime was really only popular in Hungary. I think the main reason for her new-found popularity is money...;-).
I'd say there's also been a fair amount of Habsburg nostalgia in many central European countries since 1991, which has helped them both (and Karl, whose photos I saw in a Catholic church in West Bohemia not long ago). It's interesting to speculate how different Wilhelm II's image might have been now if more of Germany had gone behind the Iron Curtain too...?
In Trieste there is a statue of Sisi in front of the railway station (itself full of photos of FJ), and a few streets away is Piazza Oberdan, named after the Italian nationalist who tried to kill Franz Josef there is the 1860s.....rather an irony!
Modified to say: FJ's age is also in issue inasmuch as it made him too old to be associated with the proto-fascist movements of the early 20h century, which he despised as vulgarly populist (e..g see his attitude to Lueger as mayor of Vienna).