There is a subtle difference between them, but I wouldn't worry about it.
You can use both of them in the same circumstance, I think it just a matter of personal preference.
However, here is what I thought about them.
"-았-" is a past making particle like "-었-"/"-였-", it means it already happened.
so "알+았+어요" can be "I got it".
On the other hand, "알+겠+어요" can mean "알+것+같아요" or "알 수 있을것 같아요". There are some usages of "-겠-", but here it is used to indicate your guess and possibilities meaning you could probably understand it in the near future.
"알겠어요" is another way to express "알았어요" indirectly and gently.
\^o^/