While I think Starcraft 2's single player is enjoyable, the story felt almost nonexistent to me. I'll give them credit, in that the CHARACTERS felt more cohesive and fleshed out. And yes, the missions actually have some unique objectives to them, instead of "oh hey, you have to level an enormous sprawling enemy base", plus the ways you could upgrade your units were interesting.

Still, the story was lacking. Almost nothing happened. The mission-to-mission dialogue is mostly explaining what the objectives are for the particular mission, but they have no greater context to the story. The only interesting story beats happen at the beginning and the end of the different mission arcs (Introduction mission arc, Colonist mission arc, Specter Tosh mission arc, Expose Mengsk mission arc, Zeratul mission arc, Gather Artifacts mission arc, Endgame mission arc).

Examples:

• you find some colonists/refugees who want to escape the sudden Zerg attacks. You help them relocate; maybe they're infected, maybe they're not. Over the course of 3 missions, nothing else of lasting importance happens.
• you find out about Tosh and the existence of Specters. You either kill all of the Specters and Tosh, or you free them and a bunch of political prisoners. Over the course of 3 missions, nothing else of lasting importance happens.
• you find out there are 5 artifact pieces, and you should get them for some reason. Also Kerrigan wants them (for a reason that is never fully explained). Over the course of 5 missions, nothing else of lasting importance happens.

When I look back on the campaign, some significant plot events happen in sudden bursts, then you kinda just stroll from one planet to another doing busywork until that particular arc concludes and something else slightly interesting happens. The three examples I gave are probably the worst examples of being mostly irrelevant filler, but not a whole lot happens in the rest of the game either.

Starcraft 1 established locations like Mar Sara, Antiga Prime, Tarsonis, Char, Korhal, Aiur, and Shakuras. I guess part of that is Blizzard only having so many tilesets to work with and trying to define a few different planets with how the maps looked, but it was evocative. Starcraft 2 revisited most of those locations, but added pretty much zero new memorable planets, since most new planets are a one-trick pony with no plot significance.

Starcraft 1 had a bunch of characters across all of the races, both allies and enemies, and a fair amount of intrigue, backstabbing, etc. Starcraft 2's new characters are largely more personally important to Raynor, but few of them really seem like major players with any lasting significance, and few do anything surprising. Tychus' betrayal was the most ridiculously obvious thing anytime he and Raynor were in the same room together. General Warfield is the most standard military leader you could possibly write. Valerian Mengsk was the only new character that took an interesting turn, though I do enjoy Tosh's personality.

I just feel like you could summarize the plot progression in a single paragraph: "Raynor finally significantly damages Mengsk's public image and there might be a rebellion or something (Wings of Liberty...I guess?), Terrans attacked Char and now Kerrigan is human, Zeratul discovers a MASSIVE ZERG RETCON and their backstory is basically that of Warcraft's Orcs now". That's about it. Tychus' betrayal subplot was moving, but it came and went and I suspect we will never hear of it again, and I don't think it will change Raynor as a character in any way. It's nothing compared to when Raynor lost Kerrigan to the Zerg, that's for sure.

Comparatively, so much more happened in Starcraft 1. I mostly mean the Terran and Protoss campaigns, where they struggle both with exterior threats and their own internal politics; admittedly, the Zerg campaign is sorely lacking characters, and is pretty much "Protect Kerrigan while she's in a chrysalis, then use Kerrigan to cause trouble for Tassadar and Zeratul on Char, then beat the shit out of Aiur". Regardless, I loved how quickly the plot moved in that game and the expansion, and how so much could change from one mission to the next, and that's sorely missing from Starcraft 2.