I've finished the main story in Heavensward, and am in the gearing up for endgame phase. So I thought it's a good point to review the expansion so far.
The main story quest is solid. It's pretty much what you want from a fantasy story. It's ironic, but it's the Japanese MMO known for catgirls which has given us a more classic western fantasy story about knights and dragons than any of the western MMOs. There are twists and turns, and the mythos of FFXIV is expanded on. It's very much a story for the fan of FFXIV, and builds on the story previously introduced.
Overall, I don't think I am a fan of the way the Ul'dah story was wrapped up, though. It's okay, but I think it was a missed opportunity. The main Ishgard story was much better.
The new zones are all good. Flying is well implemented, with a general principle of explore the zone and complete the main quests in the zone before you unlock it. FFXIV also has plenty of areas which are only accessible with flying. As well, once you have flying, quests are happy to make you wander all across the map.
There are three new classes introduced: dark knight (tank), astrologian (healer), and machinist (ranged support dps). Overall they seem interesting. However, it feels like SE erred on the side of caution, and started them off under-powered. Seeing two of the new classes in a dungeon run always makes me wince.
The dungeons and primals so far are fun and well done. I do think there should have been some minor changes in how the dungeons are distributed at endgame. Right now there are only two "expert" dungeons, but there is a third 60 story dungeon which does not have loot. It would be nice if that third dungeon was added to the expert category. On the other hand, this may be deliberate so that people can watch the cutscenes without pressure, in an attempt to avoid some of the mistakes of the original 2.0 release.
All classes got new abilities. I like the new Paladin abilities, which include two new combos for DPS, a heal, and an off-gcd move to force an automatic block
However, the paladin class story was very weak. It started off well, but then got really weird. One of the NPCs says, "This is the stupidest thing ever," and you really have to agree with him.
Heavensward is almost entirely for the max level player. The only thing a new player would get is access to the new Aura race. I would recommend that a new player wait until they hit level 50 before getting the expansion. Once you're level 50, you can get the expansion and it will allow you to earn experience and level while doing the 2.0-2.5 story.
All in all, Heavensward is "more of the same". It doesn't really make any major changes to how one plays FFXIV, just adds more of what the players like. If you liked FFXIV before, you'll like Heavensward. If you don't like FFXIV, well, it's highly unlikely you would have even gotten to the point where you can start the expansion.
I'm enjoying the expansion, and am looking forward to the next patch and continuation of the story.