Starcraft has the better style.
But Warcraft III is the better and more impressively designed and balanced game (which is saying something, considering the effort in SC balancing that was made). It also gives the casual player more scope for entertainment, unlike Starcraft which only attracted- certainly in long term- to hardcore RTS fans (though attracting very much, for sure!). The people who prefer SC are the hardcore dedicated fans who knew it inside out.
We'll see if Starcraft II- should it happen- is upped a factor in the design areas that made War III a better game from an objective point of view.
And I rather liked the storylines, even though they became predictable.