I've always preferred Zapdos, simply due to how strong and cool-looking it is, though I reckon Articuno has inched pretty close due to its design alone. To be honest, Articuno was the one whom I like catching the most, since it's just so isolated and harder to reach than the other two. I mean, with Zapdos, all you have to do is go through the power plant. There are literally no other obstacles in your way than the wild Pokemon, and they could easily be avoided with repels. Moltres was placed conveniently in your way in the Victory Road, so not really much went into hiding it. But Articuno on the other hand was placed within its own islands, located far away from everything else. Getting to it required some Strength puzzles, which I remember finding to be pretty hard as a kid. And the rush I always got when its platform appeared; it was generally awesome.
Albeit, Zapdos remains my favourite, simply because it outclasses Articuno by a tiny bit :)