Hello, Car.
Using CSS grid is more of a preference, than an advantage/disadvantage, in terms of responsiveness. Personally, I find using grid more controlled, and I always get what I want, but I am just used to it.
On the other hand, flex I find to be only more useful, when it comes to organising an unknown number of elements on a page. So, I often end up using both.
The responsiveness comes from correct use of values such as % or em. These go hand-in-hand with media-queries to determine the layout you want.
I suppose, if you do not care about specifics, flex is the way to go - ensuring no element escapes your page. But, if you want a specific layout at any time, I would recommend using grid.
Hope this helps.