Both are really fabulous islands. I would say Madagascar is much easier to visit and things are more accessible - especially the case for wildlife which is at your fingertips when you enter most parks. Seeing wildlife in New Guinea is tremendously difficult. Birds of paradise etc aside, just spotting good numbers of new species whilst walking in the forest can be a real challenge. Lodges on the PNG side I believe are more geared for tourism and should manage to show you a lot of stuff in little time, but in West Papua you need more time and determination. As for languages - you really do need at least some knowledge of indonesian in west papua unless you are being escorted by a guide. In Madagascar some french goes a long way if travelling independently.
As for culture, its a close call - both islands have fascinating cultures, although Papuas I think is more interesting. In madagascar it will probably take a lot more to really experience the native culture, but this is something I have never attempted as I have always focussed on wildlife.
All in all, in terms of time/effort versus rewarding sightings/experiences, I would say Madagascar is the more rewarding destination for most people, but it is so difficult to gauge it like that as everyone has personal interests and tastes.
Have a great trip