For larger turboprops Horn Island is fairly ****ty strip - prevailing south easterlies produce a choppy x-wind and there is some terrain to consider if a go-around is required but mostly I think it would be down to the lack of available emergency facilities. Certainly medical facilities would be very limited as that is all on Thursday Island. Also if the aircraft became disabled on the runway that would complicate engineering recovery. I would say generally, unless the immediate safety of the aircraft (fire, control problems etc.) is in jeopardy taking the aircraft to Weipa with its better infrastructure would be a better course of action.