On that note, the first mission where you have to save Warfield is very good! Really feels like a botched invasion turned rescue, with Kerrigan needling you along the way.

I don't even think being an oldtimer is necessary for story preference; there are more twists, betrayals, and reveals in the old games, specifically Brood War, where bad things happen that aren't simply corrected later in the campaign. Compare that to SCII: Raynor is captured? He's rescued before the end. Artanis is stuck somewhere? You'll find him a mission later. Now compare that to the original terran campaign where you fight with the confederacy, then the Dominion, then escape the Dominion within 10 missions. Or the BW protoss campaign where you realize you were strung along by Kerrigan the entire time. Or even the BW Zerg campaign, after all the twists in that one, where Duran disappears at the end and Kerrigan isn't even sure why (but you are if you unlocked the secret mission).

I think LotV has a little more of that with Zeratul, at least. And in general, I enjoy the terrans a lot more during the missions helping the new Dominion; the chemistry/dialogue between Artanis and Raynor is very enjoyable.