I've used Weber kettle grills for a long, long time and switched to a Kamado Joe II as a lockdown buy. Overall there's almost nothing you can do on a Kamado style barbecue that you can't do on a kettle, but there are some things that you can do better and easier.
For standard grilling tasks like burgers, steaks and chicken you'll get the same result, in fact a good sized kettle will have a larger cooking area than a Joe classic. You'd have to have a Big Joe to get the same area, and those are very expensive. With less area you have to plan a bit more, it hasn't been an issue with me.
The two areas where the kamado excels are in very high heat applications like pizza making and low heat applications like smoking. I've made pizza on a weber and gotten decent but not outstanding results, where on the kamado I've made pizza as good as I've had in Naples as it can get ferociously hot. There are all sorts of expensive, specialized add-ons for that but I just put my pizza stone on the top rack and it works great.
I've smoked on a weber, and it's doable, but a lot of work for a long smoke. It's hard to keep it on a precise temperature, and you have to top off the charcoal for longer smoking times. When you add charcoal through the side slots in the weber (presuming you have them) it's too easy to get soot all over the food, I found I had to take the whole top rack off and put it aside to refill it, which is a pain to do, and then you have to fiddle with the air vents loads to get the temperature right again.
The kamado is easy to get to a precise temperature due to airflow control and it is very efficient due to the ceramic insulation so the charcoal lasts a whole day, I've never had to add any even when I'm doing a 16 hour smoke on large brisket. All the baffles and the flexible rack system the Joe comes with is very helpful in creating the indirect heating as well.
I know of people who have used firebrick to create some heat baffling in kettle grills, which helps control the fluctuations somewhat, it doesn't help with refilling though.
One major consideration is weight: the kamado is heavy, it takes 2 people to lift it as it's metal and ceramic. It rolls just fine on a flat surface, but if you needed to move it around a lot it's going to be tough. A weber is very transportable.