Dragonrealms is more fun for a few reasons:
Better feedback on your character's progress. There's this kind of instant gratification to training skills in Dragonrealms; you swim through across a river and you can see that your swimming ability just got better through practice. Melee with some rats for a while, and you notice a marked improvement in your ability to attack them and defend against them. You see this in actual performance as well as in numbers when you type EXP to check your experience.
In Achaea, actually using a magic skill never seemed to make my character better at using magic, and one of the only types of growth I got to see was how many more percent I had to go to get to the next level. For that matter, at level 10, I was still having some trouble with the same creatures (rats) that I started out hunting. This lack of feedback seems like it might actually point to a less developed experience and character advancement system.
Simplicity. Dragonrealms is less complex for a newbie to figure out--there are fewer guilds and fewer races. An emphasis is put on developing your character as you see fit, with an emphasis on role-playing. That said, behind the scenes, the programming that runs Dragonrealms strikes me as more developed, with systems for combat and skills that are interdependent--simply doing things in Dragonrealms seems to be smoother and makes more sense.
In Achea, you can actually write your own character description, which is cool, but I felt like I didn't have to roleplay to communicate this description. That, and in Achaea, there were many guilds that were essentially the same, some just came off as evil and some as good. And, while there were many, many ways to attack a rat, only one way (punching) actually seemed to work fast enough to kill them before they killed my character.
Teamwork and community. Early on in Dragonrealms, you begin to realize that there is a community you are part of. Others help you out, some ask to join you on a hunting trip. Truly, there is safety in small groups, and many new characters form bonds that turn into long-term relationships with hunting partners and friends.
Achaea is more individualistic. You can actually rely on your own hunting prowess, and there is this expectation that you will engage in player-vs-player combat at some point. While there are chat channels open for newbies, your guild, and the city you belong to, most often it is just people asking questions and saying "hi" or "bye". Those are weak bonds, compared to the relationships that get formed in Dragonrealms through shared experiences.