I'm not a Chrome-by-default user. But when it is closed and I drag a link to its icon, it is very infuriating that it just doesn't open the link that I asked it to, but whatever else it felt like opening alongside it.
You can disable the "open all the tabs I had open last time" behavior in the settings, though. Is Firefox more clairvoyant about what you want (e.g., startup with arguments does not load prior tabs, but normal startup does)?