While neither game is perfect IMO, letting the game mature without micromanaging it was a very important aspect of SCBW's success. Instead of mucking with units on a monthly basis they let things simmer and ultimately let balance be achieved through proper map design used in the competitive scene.
In my personal opinion one of the biggest faults with SC2 was their unit design philosophy. The idea that every unit was viable or had some special unlock created a balance nightmare. Its been years since I played either game competitively (played iCCup in BW / Collegiate StarLeague for SC2:WoL) but I remember always feeling like the game had too much "gotcha" in it that SCBW never had. Didn't scout proxy reapers? gg. Didn't scout fast void? gg. Didn't scout x? gg. It was too much rock-paper-scissors where missing one piece of intel was death while SCBW wasn't entirely the same. Taking the Terran/Protoss matchup for example you'd typically expect the early game to be vulture+tank vs. zealot+goon where if the terran player just a-moved into the protoss it was guaranteed loss, but microing the vulture and tanks gave you the chance and arguably the upperhand where the skill of the either player determined the outcome. SC2 didn't have that to the same extent.
So SC2 starts off with SCV-auto split, no more manual splitting at the start of the game (all players now can play the first 5-seconds of every game like a pro: no practice needed anymore) But then muscle-memory people wanted an edge, so they added MULEs / Spawn Larva / Chronoboost, giving players a muscle-memory / simple timer countdown to play with. Etc. etc.
Just back-and-forth changes like that was the real problem. The general balance patches had no idea for the final metagame they were actually going for. Did Blizzard want a game that rewarded manual effort (Juggle MULEs?)? Or did they want a game where manual-effort was minimized (Auto-Worker Split?)
In the end: Blizzard wanted both, even if the two designs contradicted each other. You really can't please both groups of players, but by switching back and forth between the two designs, they only really pissed off both camps over the long term.
Starcraft 2 added "Archon Mode", where you can 2vs1 (Weak+Weak player vs Strong player), controlling the same team. There were far more opportunities to play teams in Starcraft2 than Brood War.
And the 2v2 was always an option in Starcraft 2 anyway.
Starcraft 2 units really do "what you want" most of the time: automatically balling up into groups or "dancing" together. From one perspective, elite Starcraft1 players who memorized "The Magic Box" and other engine-level pathfinding behaviors saw this as an abomination: other players can gain the same skills now without practice.
On the other hand... lets be frank. Dragoon / Goliath pathfinding was bullshit from Starcraft1. The extraordinary measures you'd have to take to become a competitive player who uses those (ie: Magic box memorization. Dragoon Dance practice. Etc. etc.) was fundamentally unfun.
This is coming from me: someone who did put in the effort to properly dragoon dance / Muta stack / etc. etc. We all do things to seek a competitive edge against our opponents.
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The work / reward ratio needs to be there in some extent. But it can't be so large to turn beginners away. I'm not sure if anyone's found the proper balance yet, but Starcraft2 definitely was better from that perspective.
EDIT: I'm also a big fan of fighting games. Hyper-fighters, like Blazblue or Guilty Gear, have a nice auto-balance called combo proration. Combos are clearly the best way to play, but each combo makes the rest of the combo exponentially do less damage (!!!). This means that a 50 hit combo in BlazBlue will probably only do 10% more than a 20 hit combo, despite the huge difficulty curve in executing. The bulk of the damage is from the attacks before proration kicks in. This allows for the expert-community to practice for those 50-hit combos, while not necessarily granting huge 250% bonuses over beginners. A casual player may only decide to learn the 20-hit combo and still be 90% of the way to playing like an expert (compared to experts who have to work far, far harder to get the last 10% of damage).