Understand my poor English : ( let me answer your question.
Basically, both words have same meaning. 겁니다 is short for 것 입니다. It is not standard language actually. I recommend you to use 것 입니다.
Imagine this situation, if someone ask you like this 'what are you going to do?' so whoever does you can just answer like this
ex) I will play the video game.
but as you already know there is honorific in Korean.
When you answer your friend = 나 는 게임을 하겠다.(할것이다, when you saying 할거야)
When you answer your mom and father or someone else is older than you
= 저 는 게임을 할 것 입니다.(겁니다, 거예요)
can you understand my explanation? I`m sorry i`m not good at English : (
If you want more information send a message to me so i will do my best to answer you.