What are the benefits of using contactless payment cards for travel on TfL services?

There are plenty. You can travel without using or topping up an Oyster card in advance, and it’s cheaper than paying by cash. You can also use buses, Tubes and trams without spending time choosing a ticket, and you can benefit from daily (as well as Monday to Sunday) capping. 

At this moment in time, you can’t buy monthly and longer period Travelcards and Bus & Tram Passes with contactless cards.