In most contexts, "обычно" means more often than "часто".
But this is not coming from an inherent meaning of those words - it's rather a "byproduct" of their meaning. As @shabunc had illustrated:
- "обычно" = "usually"
- "часто" = "often"
"Usually" implies that in a certain situation there is a typical flow of events, which frequency can be qualified as "usually".
Now if we take the same certain situation and change qualifier to "frequently", that changes the meaning, implying that there's more than one typical flow of events, and "frequent" one corresponds to the one that is the most common - which would be less frequent if there was only one typical flow.
Of course we have to compare "apples to apples". "Обычно" and "часто" cannot be compared if we are talking about different situations.