You do need special lights. Dynamos put out AC power, which will need to be converted to DC if you are using LEDs. Incandescent and halogen lights don't need this, but they're on their way out. Good dynamo lights also have a capacitor (called a "standlight") which will keep the lights for a few minutes while you are stopped. Some will also have a light sensor that will turn them on automatically when it gets dark.

As for advantages, you've got it. Dynamo lights never need to be recharged. This isn't a big deal for "be seen" lights, since you will get months out of a battery with modern LEDs. However, a light bright enough to see by (like modern dynamo lights) will have a much shorter battery life, and so will generally need to be charged every night. Whether this is enough of a hassle to spend the extra money on a dynamo system is up to you.

Also, there are two kinds of dynamos. Bottle dynamos bolt on to the frame and are run by rubbing against the tire. These are cheap and can be completely disconnected when not using the lights, but will have noticeable drag when on and are prone to slipping in wet weather. Dynohubs use magnets built into the hub of the front wheel. These are more expensive, but they do not slip and are extremely efficient since they incur no mechanical losses. There will always be some drag with a hub dynamo, even with the lights off, but it is slight enough to be imperceptible to most people.

(Personally, I'm currently using battery lights, except for the vintage dynohub on my Raleigh Superbe. However, I am planning to move my bikes over to dynamos eventually.)