For me I like it for two reasons.
1. The first 'act' of the story ending with the first dungeon did a good job of setting up the world and sense of hopelessness, and then finally restoring a bit of hope by defeating the first Lightwarden. I like this part of the story.
2. Emet-Selch and the final msq zone.
3. Okay a third thing, Arbert. I loved all the scenes with him.
These two things help prop it up. I do think the story drags down some between these two points.
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Oh and also, part of is because SB's msq was....worse. I thought 4.0 was very disapointing, and while I liked 4.1, 4.2 and 4.3 made me want to gag. So even just having a solid/decent story is an upgrade over Stormblood.