Shoes or boots, at least as far as outdoors goes serve only one purpose-protect your feet. So, whatever works for you for that purpose is what you need. I've hiked in plastic climbing boots, full leather boots, lightweight boots and running shoes/cross-trainers. Each have their advantages and disadvantages. In my experience running shoes are comfortable but offer little protection and little or no ankle support; lightweight boots offer better ankle support and my full leather boots offer the most protection for the weight. Plastic boots are for winter, so I am discounting them here.

With a pack, I like a boot because I have a suspect ankle that seems to be fine most of the time, but I have no interest in testing it. I have also worn my leather boots on trails that would have shredded my running shoes because of the loose sharp rocks I was wading through at times.