A Fundamentally Different Diablo III
Let's be clear: Reaper of Souls is still in beta, which means there's plenty of mechanics that aren't working at the moment. Crafting is still a work in progress. Game balance continues to change significantly from patch to patch. Some new character abilities aren't implemented yet. There are encounters that need tweaking and class mechanics that should probably be revisited. Certain mechanics aren't functional, or aren't functioning correctly.
For all of that, the new game is far more fun than classic Diablo 3. Higher drop rates and the new Adventure Mode make it easy to leap into a game and run a quick dungeon or pair up with friends for an evening of demon carnage. If you liked the Paladin from Diablo II, you'll likely love the Crusader, and the two classes share a common storyline according to in-game lore.
Reaper of Soul's new Adventure Mode is a great way to experience the game in small slices while still working towards rewards. Sharing Paragon levels between classes means that's you aren't starting over completely when you roll a new character type, and while the gains from each Paragon level are small, leveling is fast enough that they add up. Mostly, though, what Reaper of Souls adds is a classic blast of fun. Legendary drop rates are high enough that the next critter you kill might actually be carrying something useful. Paragon levels give you a way to carry meaningful improvements to a new type of character. Each character can allocate these points independently -- earn 31 Paragon levels on a Barbarian and your Wizard gets to spend those levels any way he likes.
The fact that Bounties vary from Act to Act means that replaying the game isn't as deadly dull as the old method of progressing linearly through one area or repeating the same area over, and over, and over. Meanwhile, the new legendary item designs seem to suggest that Blizzard is serious about enabling alternate playstyles or advancement methods.
These changes aren't going to fix some of the design issues that other players have raised: If you don't like Diablo 3's skill trees, or wish the game allowed for modding, or want damage scaling to be independent of weapon damage, than these shifts aren't going to remake the game for you.