How are the servers different?

Answer

The server differences are mostly historical now, with the exception of Ken Rauhel, which is a non player-vs-player server. We'll take you through a little history and explain some of the terminology.

Depardieu & Ken Rauhel
Depardieu (or Dep) was the first official US-based Lineage server and is therefor the oldest. Shortly after it's launch, the Ken Rauhel Server was created.

Ken Rauhel (or Ken) is a non Player-vs-Player server - it's most distinguishing difference is that it is not possible to randomly attack and kill other players during normal game-play. There are a few exceptions to this rule - any combat zones are still PVP areas, as are castle grounds and the areas surrounding them - however, outside of a castle siege no experience points are lost in PvP combat.

The Lands of Aden
The Lands of Aden (or LoA) was introduced in November of 2002 as a server for new players and people that were new to online gaming. Additional focus was put into the new-player areas and the game balance was altered to create an easier, more palatable gaming experience for the US audience.

The new Lands of Aden server was a success, and many players flocked to it to reap the rewards of a more relaxed gaming-style.

Splat
Early 2006 saw an event that landed a few LoA-style items on the traditional "Korean-style" servers Dep & Ken. What nobody realised was that this was the beginning of the end.

On August 16th 2006, NCsoft shocked the community by revealing the beginning of their plans to cover all US servers with the same play-style as their Lands of Aden server. Just a few weeks later the full US-Ruleset was applied.

What the hell is the difference between Dep & LoA?
Well, now you know that Ken is a non-PvP server and that Dep & LoA are both PvP. There's one final difference between Depardieu and The Lands of Aden... Hell. Depardieu, mostly populated by mass-murdering cretins - or hard-core gamers, objected heavily to the introduction of Hell on their server, so it was removed.

Does that mean there's no PvP scene on Ken?
No, it doesn't. The PvP scene on Ken is actually quite active. Players have to be slightly more creative in their genocide of others, but the Ken folks still occasionally rise up and riot.

What of it all?
What is all boils down to (other than the choice of PvP or non-PvP) is age. Most of the Ken & Dep folks have been playing their characters for a long time under a more strenuous set of game-rules. A few of the LoA folks will, of course, argue that they gave up their characters to jump servers too - tho given the length of time under the different rulesets, it's probably all evened out by now anyway.

Where should I play?
Wherever the heck you like. In to blood-sports? Play Dep. Want to kill your friends and burn in Hell? Play LoA. Want to cower behind a rock when a war breaks out, or just enjoy a peaceful hunting experience with your buddies? Play Ken.