I like certain... parts of the story. I like Y'shtola and Urianger. Some of the job quests were pretty good (particularly BRD and BLM). But there are two main components to why I feel like this story is all-around unimpressive.

1. The presentation. The cutscenes are so static. Any emotion characters should be feeling is completely stifled by the unnatural delays caused by either having to click through dialogue or these weird delays in expression that are built into the cutscene. A character will say something, and then it cuts to another character for reaction, and there's this couple second pause before their face twists into this unnaturally exaggerated surprised expression or somesuch. And if I tried to count the number of times SE tried to convey a serious interaction by having two characters take ten seconds each to stiffly nod at each other and then walk away like mannequins, I'd run out of fingers and toes. The voice acting leaves much to be desired as well, with some exceptions. But overall, the story is hindered by wooden cutscenes that disrupt the flow of conversation.

2. The quality of the writing. I'll set aside for now the hilarity that is how many characters in the story have white hair (my husband and I joke about it constantly). But the characters themselves really haven't grabbed me, with a few exceptions. Y'shtola is one, who steps out of a bland shell with the firm (and importantly: consistent) characteristic of her opinions on the Grand Companies' treatment of the beast tribes. Urianger has been handled well so far, starting out as a quiet book nerd we know little about, and SE has actually introduced hidden pieces of his personality and given him depth in a pretty natural progression. He could have easily remained that static archetype, but he doesn't and it's well done. I also enjoyed Aymeric's introduction in ARR and thought his character presentation balanced snobby traits with an underlying compassionate lean nicely. But those things are the exception to the rule. For the most part, characters are bland and predictable.

In addition to the characters, the plot itself leaves much to be desired. I won't go into detail about how sluggish and dull the ARR story is (and how poorly presented it is through unending fetch quests) - I think that's something many people in this thread have already touched on. What I will turn to as an example instead is peculiar and nonsensical plot choices. ARR's storyline is awash with missed opportunities to create a much more interesting and complex story. Thancred's "betrayal" is a great example. Instead of pulling a cheat card out of their butts, they missed the opportunity to really subvert the Scions' story in the Thancred/Ascian plot. Thancred was exhausting himself. Take that a step further and portray him struggling with a fight that seems futile. His struggle is so great that he begins wondering if all their fighting is for naught. This alone would be enough of an opening for an Ascian to begin influencing him, but I think an important point to make would be that Thancred's actions aren't JUST the will of an Ascian puppeteer. It was Thancred's own feelings that originally stirred him, and these should come to light. As he performs one minor sabotage after another toward the Scions, disrupting their own struggles against the Garleans, Thancred on his own becomes more and more sure that it's simply not worth fighting anymore. That they can save far more lives by allowing the Garleans to conquer than they would by resisting. At this point him and the Ascian are pretty much working together. This, in the end, would make the reveal that much more dramatic. The Scions would still try to save him, still try to rescue Thancred from what they perceive to be Ascian control. But then when they do expel the Ascian from his body, the blow is all the greater when Thancred reveals his own motivations. The Scions' feelings of betrayal and grief for Thancred would be countered by his belief that he's doing the right thing for Eorzea. Such a dichotomy would have a much greater impact than the very simple, "Oh, it was just the evil Ascian and now everything is better!" tripe that we got in the actual story.

That's one example, but there are a number of such poor story choices made by SE where they took an easy out to quickly resolve what should have been (and COULD have been) a very complicated and multi-faceted issue.

The Garleans alone are nothing but a toothless specter for the most part, which is a shame all on its own. SE never quite figures out how to make them the terrifying, dominating force that they are claimed to be in dialogue by more than a few characters. And that's one big problem: SE's story is inconsistent in how characters react vs how the story is written.

Specific to Heavensward, I also find that SE's decision to heavy-handedly lay every single Evil Catholic Church stereotype in existence upon Ishgard as just utterly unnecessary and really damages my ability to connect with the story. Oh, of course the Fantasy Pope is secretly evil. Oh, of course the Fantasy Church is restricting people's access to information (see as an example the Galileo plot copy of the AST quests, which gets the whole Galileo thing wrong anyway because the Church actually funded his research quite happily). Oh, of course they have "Inquisitors" who are pretty much universally and exaggeratedly cruel and harsh about their judgments. Oh, of course Fantasy Religion are the bad guys and us Pure Spiritual Outsiders are going to make everyone see the light. I could go on, but to sum it up: it's a cheap ploy to set up another Big Bad. They could easily tell the story of the Ishgard-dragon war without turning Ishgard into an obnoxious and stereotypical caricature of Catholicism.

And, uhm... I feel like my post has gone on long enough so I'll stop there. To be honest, there are a lot of other plot points I could bring up, but I think I've hit the main points. xD