It's definitely not as good. I hear that even the Korean pros still played SC1 over 2 for some reason? I'm not good enough to understand if the gameplay is better. I did like the progression in campaign with Heart of the Swarm from what I remember.
I can't help but feel it is a little bit out of nostalgia.
Here are some of the improvements that have been implemented.
-You can select more than twelve units at once.
-Units with special abilities don't get "buried" when you select multiple units. You don't have to select them individually if you want to make use of their abilities. (you can for example have a group of Goliaths and Siege Tanks and make the tanks go in deploy mode without having to deselect the Goliaths.
-Units with special abilities don't use them all at once when you have selected them and want to use an ability such as that Protoss psionic storm. Instead you just have to select the power once again and then another Protoss uses that ability.
-Those Protoss units that make their own smaller units such as the carrier and its interceptors can be set on automatic so that they immediately start making those instead of being ordered to do so.
Sorry but the story really is bad. It starts of well in WoL though there are some retcons and changes already at the start.
-Raynor instead of wanting to kill Kerrigan for killing Fenix and so many others now behaves as a love sick puppy.
-The Terran Dominion is fully rebuilt after the UED and the Zerg trashed it quite well several years ago.
-Arcturus wants Raynor assassinated. Sure Arcturus was pissed at Raynor at the end of the Terran campaign of SC1 for leaving, but Raynor did save Arcturus' life during Brood War.
-In the meanwhile it was revealed that the Overmind was never its own agent, he was actually secretly controlled by an outside force; Amon, a fallen Xel'naga.
-The Xel'naga have been changed from alien scientists similar to the Pilots/Engineers of Alien, into gods that come from a parallel universe and who created the physical universe in which we exist.
-Kerrigan is also controlled by Amon, she never became "evil" out of her own volition. That did not stop her from killing millions once again after she had turned "good" and made the Zerg overrun Terran worlds.
-Protoss are retconned not to be the purity of form, us Terrans now are despite that the Xel'naga did not engineer the Terrans.
I know the lore of Starcraft never was very good as it borrows openly from many sources but if the writers can not even stick to their own lore for its sequel just because they want to insert new plot elements.
They could still have their evil Xel'naga without making it a god, or that Raynor and Arcturus had a feud though the Dominion would not be the super power that it was in SC2.
But Kerrigan being deinfested was done because Metzen or someone else wanted a Raynor-Kerrigan love story.
And I am not going to tell you what Kerrigan's final outcome is.
Edit:
Okay the balancing issues
BigGuyCIA brings up play the biggest role. I never played this game in multiplayer mode so I do not know how unbalanced the sides are when controlled by human players.