How are raid reward distributed?

I kind of know that higher tiered raid has better reward bundle, but not sure how exactly it works. As a minority group for the most occasions, is it more beneficial to solo Tier 3 or duo Tier 4? Also, my wife and I usually play together. In the case of Tier 3, is it better for us to solo separately or there's no difference that we can simply duo it, in turn of rewards (by duoing it we surely have more balls but it's usually not an issue to catch the boss)?