Diplomacy may be the rare game that's better played by mail or email than in-person, although it truly is a classic game no matter which way it's played.
Still, the nature of Diplomacy creates some problems for face-to-face play that are avoided when played remotely, while remote play also brings advantages over playing on the table top.
First among those is that it's far easier to organize a game via remote media than face-to-face play. A satisfying game of Diplomacy really requires that all seven powers be played by competitors with reasonably comparable skill and knowledge. It's hard to get seven players together for face-to-face play, let alone seven strong players. Outside of conventions or perhaps game clubs in major metro areas, the only place I've seen it happen fairly often is on college campuses, which provide a sufficiently large pool of intelligent, educated folks with a fair amount of time on their hands. In face-to-face play it's generally easy to spot any players who are newbies and take advantage of them. Remote play, whether by snail mail (rare these days) or email allows a game organizer to quickly match seven interested players and the normally anonymous nature of player identity can mask the presence of weaker or newer players long enough that they have a chance to learn without necessarily being picked on.
A second advantage of remote play over face-to-face play is time. Diplomacy can be a long game, even with just 15 minutes allocated for negotiating sessions. Adjudicating moves can take a considerable amount of time in complicated situations. Face-to-face play hinders negotiations because it's hard to hide who is talking to who. Remote play generally means a lot more time is available for negotiations and it's possible for an energetic player to keep up a steady stream of correspondence with everybody. Overall game length is less of a problem because it can be spread in very small packets of time over weeks or months instead of taking up a whole day.
A third advantage of remote play is that it solves the player-elimination problem. Not by preventing players from being eliminated, of course, but by mitigating its effect. In a face-to-face game it's not uncommon for one or more players to get knocked out of the game early. When this happens there's now the problem of what they're to do while the game continues without them. If two players happen to get eliminated about the same time they might play something else, but if not then someone will probably be going home early. With remote play this isn't a problem because eliminated players can merely join another game, if they'd like, and get right back into things, perhaps a little wiser.
A fourth advantage of remote play is a better quality of play. With more time to think, there's less of a chance for mistakes in order writing or bad play. Most remote play has some sort of adjudication protocol or software that will ensure that complicated adjudications are done in accordance with the rules. Even play-by-mail unusually uses a gamemaster who can figure it all out. A site like Bounced will even flag illegal orders before they're sent. In contrast, face-to-face play is often marred by poorly written orders and mistakes.
About the only way in which face-to-face Diplomacy is better is the opportunity it provides for social banter and personal interaction. Games that allow press or other forms of public communication between players can mitigate this a bit, but I think it's fair to say that it's still hard to beat face-to-face play for the personal touch. With two-player wargames this can be a decisive advantage, but I think for Diplomacy the previously mentioned factors shift the advantage to the side of remote-style play.