How do you identify which one caused it? Does it immediately trip the main again when you put the offending breaker on, ie the fault is still there? If so, if it's not intermittent, I would think you'd immediately further track down what the source of the fault is.
Do you really mean tripping or that it's something on that 63A breaker that causes the main to trip? You said the main was tripping, not the other breaker. Also this picture is different than what I think most of us were envisioning, which was a typical main panel with individual branch circuits, not a main that feeds what appears to be two subpanels, That shouldn't really matter though.
What do you believe the total load normal load on it is, just before it trips? What's going on at the subpanels when this happens, those 63A breakers must feed subpanels of some kind. Anything tripped there? As to why the 75A trips first, it makes more sense now. Breakers have curves as to how fast they trip versus the size of the fault. Different breakers will have different curves and they are not exact. What you have is a 63A breaker and a 75A both exposed to an overload. Additionally, you don't tell us what else is on that main panel besides the two 63A breakers, but if there are other circuits, then the 75A is seeing whatever the 63A one is, plus those other loads. With other loads, no surprise it trips first. Even without other loads, if you present a major over load to both, the 75A might trip first if it's curve is slightly different.
I think most of us were envisioning that you had a big main breaker, eg 150A and then smaller breakers, eg 20A that feed those other circuits.
Where are you? We were assuming this is US.