Avalon Hill board games are better than other games because of their strategy, their replayability, and their focus on tactical skills and strategic decision making. In most games, you can recover from a mistake or two, but not from too many. On the other hand, unlike Settlers of Catan, you still can recover and win from behind, especially in Diplomacy. Also once you've played Settlers four or five times, you are just repeating games, which is why they had to come up with so many new rules and scenarios. In Diplomacy, I've rarely replayed the same game, and even so the diplomatic field is always different.
Back to Avalon Hill games though. Diplomacy is still better than the other Avalon Hill based board games I like play (Third Reich/ATR/AWAW and Squad Leader/ASL) because
1. It's easier to find players.
2. The rules are simpler so, well, it's easier to find players.
3. Webdiplomacy exists and has a huge player base so, it's easy to find players.
4. Everything everyone else said (no dice/cards, no turns, your destiny is to some extent in your own hands, and if it's not, the destiny of other players who robbed you of yours is often in your hands.) thus it's easy to find players.
The only reason I keep going back to the Squad Leader and Third Reich genre games is that they are so much deeper strategically and tactically than Diplomacy, but their biggest downfall is the lack of players.. And nothing beats the fleet combat system in AWAW.