For me it's always a toss up between DKC2 and DKC3. The first game is too antiquated and straightforward by comparison - no DK Coins, no Bonus levels, no real incentive for replaying levels or finding all the secrets except for winning extra lives. By the second game I like how the game keeps track of each level's "completion" and by the third game I like the addition of RPG-ish trade quests in order to unlock more content and ultimately the "real" ending of the game.
So there's an evolution in terms of richness and complexity and by that rationale the third game is probably the better one (it's way more polished, that's for sure). Having said that I probably like DKC2 the best. Each world has a unique theme (pirate world, lava world, swamp world, cemetery world, etc) that is more interesting and appealing that the usual grasslands/desert/cavern/forest/ice world/fire world/techno world malarkey from Mario & Sonic, and I like the somber tone of the game. It has some of my favorite compositions from the trilogy too. The only flaw I see (I think) is that Dixie and Diddy are pretty same-y in terms of gameplay, as far as I recall. Was Diddy stronger, like DK from 1 and Kiddy from 3? I forget.