(as I understood) Since 어/아/여 봤어요 is about trying something, it can be used only if you wanted to do something and did it (for example 한국에 가 봤어요. - I visited Korea (I wanted to go there and I went there)) and -은/ㄴ적이 있어요 can be also used in a negative context (such as 지갑을 잃어버린 적 있어요 - I've lost my wallet once (i didn't want to have this kind of experience but it happened to me anyway). Imagine "have you ever done smth" construction in English, I think they are quite similar with -은/ㄴ 적이 있어요 :)
