Queuing up for all of the difficulties across various characters since RoS release, here is my experience with public games:
Normal: People split farming Act 1 bounties. Everyone leaves and the game ends once all bounties are done and the cache is collected. Farming for Ring of Royal Grandeur.
Hard - Master: Random act bounties and people seem to be farming special crafting mats sometimes, angelic shards for example. Sometimes a rift opens but it's rare.
T1 - Paragon 50-200's rifting. Lots of game hopping of people looking for rifts in progress, but one usually opens within 1-2 minutes of joining, so not sure why people join then leave instantly. Fast rift runs but not a lot of legendary loot. Mostly just for forgotten soul farming.
T2 - Paragon 2-80's who sit around waiting for someone with keys to open a rift and carry them to loot. Rifts go slow because you're in a game with a bunch of leeches looking to be carried. Did this difficulty for a few days then switched to T3 when I realized T3 was faster clears.
T3 - Paragon 200-400 players who do fast rifts. Anyone below paragon 100 is generally kicked pretty quickly. Lots of legendary drops. Less deaths than T2 because on T2 everyone is a bunch of incompetent carries that die all the time so you effectively solo rifts.
No experience with T4+ public games, kinda scared to queue up for them, usually save that for game with friends/clan.