Everything said so far is correct. 
Smartthings can control Z wave and zigbee devices, Plus some additional cloud integrations, but has no way to send IR commands. Adding harmony gives you control over IR devices, both home theater stuff and some air-conditioners and fans with IR remotes.
There is an additional device called the “harmony hub extender” which has some Z wave and zigbee, but if you use that you can’t use SmartThings with those devices. And the harmony device is really simplistic, it’s mostly just intended to let you use motion sensors with your home theater. For a more complete discussion of that device see the following, but the short answer is if you have SmartThings you don’t need the hub extender.
So then the question is what would smartthings give you that just harmony plus its own hub extender wouldn’t, and that answer is very clear: SmartThings is way smarter. Just as one example, harmony will not let you unlock a lock if you’re not at home. Not even with IFTTT. SmartThings will, so you can use it to unlock the door when a holiday guest calls to tell you they’ve arrived, for example.
Smartthings also lets you just do a lot more. For example, there is no way with harmony to get a message if a door is left open, whether it’s at a particular time of day or for a duration longer than five minutes. With the harmony extender you could have opening the door cause the lights to come on. But you can’t get any notifications at all.
So the shortest short answer is that if you have SmartThings, you don’t need the harmony hub extender. And if you use the Harmony hub extender you can’t use SmartThings with those devices. But if you have just the harmony hub and the smartthings hub, you add an additional set of devices to each, and you get to take advantage of SmartThings’ much more sophisticated scheduling options.