Still, I don't really get the context where this set should be used over the other one.
could anyone provide examples with explanations please?
OK, I will give it a shot.
私は歌が上手です。
私は歌が得意です。
Although the two mean the same thing (I am good at singing), the latter has just a hint of modesty in it. You are not saying flat out that you sing well.
上手/下手 can only be determined by others while you yourself can assess 得意/苦手 about yourself.
Now, having said that, I know some of you say that you hear ppl say all the time 「私は＿＿＿が下手です。」.
While it is a no-no to boast about your singing prowess, it is OK to put yourself down.
Also, only YOU know for real if you really are 得意/苦手 about something. Because even when you find something a piece of cake (得意）、the end result from other ppl's perspectives cannot be always positive. Even if you find something very hard to do (苦手）, chances are you are capable of producing steller results. So, you can use 得意/苦手 only when you are talking about yourself.
Let's say you just performed a very passionate rendition of My Heart Will Go On in front of me. I may compliment you on your singing by saying 「Ｄｒｅａｍｅｒは歌が上手ですね」 but I would NOT say 「Ｄｒｅａｍｅｒは歌が得意ですね」 because I wouldn't know that. All I know is what came out of your mouth sounded good. I wouldn't know if it came easily to you or you had a very hard time making it sound good. You might reply 「どうもありがとう。私はこの歌が得意なんです」 or turn on the Modesty Machine and say 「そんなことないですよ～。 下手だったでしょう？ 苦手なんです、歌は。」.