I've never enjoyed the birds as much as Entei/Raikou/Suicune. However Zapdos is probably (just) still my favourite, mainly due to it looking badass on my friend's pokémon card when I was younger. Moltres is a good battler, but I don't like its design much - especially compared with Charizard - although it does look slightly better in Gen IV. Articuno is the least interesting in my opinion, although its design is nicer than that of Moltres. The movepool of all three isn't exactly bad...it just seems a little lacking in-game, and seeing as nobody battles competitively in Gen III, that's all that matters right?
...actually, now I've looked at them, I'm definitely throwing a Zapdos into my LeafGreen team next time I play...