API driven campaign with audience driven by call

I'd say this depends on whether you are going to be segmenting on static or dynamic values. If the segment filters can be created using static values e.g., (some_value >= 99 etc) then you are probably better using segments / filters in the canvas or campaign UI as they'll be easier to see and manage going forward.

However if you want to segment or filter on dynamic values then I don't think this is possible via the UI (unfortunately we can't use liquid in filters) so in that case you'd probably want to use connected audience filters in your API call to filter on the dynamic values (e.g, some_property >= some_variable) etc. It would be nice if we could do more dynamic filtering in the UI, but it seems as if connected audience filters are the way to go here. Much more of a coding burden in using connected audience filters though - but if you are triggering via API calls anyway then it's maybe not so bad to pass in some connected audience data.