The biggest problem with Warcraft III, aside from its silly storyline and hammy writing (which is arguably more down to personal preference), at least for me, was its extreme focus on micro-management. Okay, so it may not quite be high-level StarCraft play, but so much of Warcraft III felt to me not so much about building the right units, build order, managing resources etc., but rather all about who can click fastest, who can polymorph the most enemies, etc.
If anything it brings out the inherent limitations of the RTS genre: if you have a game that relies less on things like planning and, you know, strategy, and more on tactics, then the real-time component of the game can serve as a detriment to playability but all but the most Korean of players. It's this that also turns me off of StarCraft, and draws me more towards Command & Conquer (which, to be fair, suffers from tank rushing etc.), Total Annihilation, Company of Heroes and Dawn of War (which make up for the micro requirement by downplaying other gameplay components and keeping things simple), as well as turn-based titles like Heroes and Civilization. For me, an RTS can be fast and exciting, but when success comes down more to reflexes, ping times, and whether your allies are stupid or not, it's crossed a threshold that I'm not really willing to go beyond.
Admittedly, I did have fun with Warcraft III. There were some damn good custom games, including thousands of tower and hero defense maps, DotA, silly mini-game collections like Uther Party, etc., and for what it was, the campaign was pretty enjoyable. But the strength of that game is in its community and custom games, not in any brilliant mechanics.