SC2 is very much the same thing with improvements in all areas. The graphics are awesome though mind you, you need a decent graphics card to play on ultra with a smooth fps. I use a GeForce GTX 660 (A$200) and it gives me about 100 fps on average on ultra. Of course this goes up and down depending on how many units are on screen.
The campaign is actually quite interesting as it's got a variety of missions. It's the not boring SC1 campaigns which are pretty much the same thing over and over again. My only critique is the way they've animated the way characters walk in between missions... just a little too much hip movement for men ;P
With SC2, the multiplayer is brilliant and I haven't had issues at all playing on battle.net. I hook onto the EU region to play with friends. I do miss some of the units on multiplayer as it is limited - that's my only critique. It is very clear in this game who are the newbs and everyone that plays it and does their homework can easily go up the ladder as there are clear strategies out there.
I'm one of the newbs!