The two sentences have a quite different meaning: "etwas in den Griff bekommen" means to get the hang of something, so that you can use it well. "Sich an etwas gewöhnen" means to get used to something.
Er hat sich ans Wetter gewöhnt.
Means he got used to the weather, i.e. by knowing that he has to wear a coat.
Er hat das Wetter in den Griff bekommen.
This sounds really odd, because normally there's nothing you can do about the weather. But colloquially, this is also used to express the same, especially when it means that he is now able go cope with the (bad) weather.