I'd say のに is used much more commonly than this pattern, and this pattern also seems to be used for more serious things - のに might be something like 速く出かけたのに道路が込んでいて遅れてしまった (Even though I left early, there was traffic and I was late), にもかかわらず would be more like 貧困にもかかわらず棟大で勉強することができた (Despite poverty he was able to study at Tokyo University) - so のに would be more casual, にもかかわらず more serious (although I wouldn't necessarily call it more *formal*...)