There are four cases that tend to be considered in this decision for any person who truly wants to enjoy Japanese entertainment. Obviously it can be easily answered if you don't want to read the book, the dubbed anime is for you, of course I will assume you want to either have Japanese anime (subtitled or not) and manga (translated or not). I expect you to take into account "availability" or price already. I would never buy a thousand dollar anime if I can have the manga for ten dollars.

In case your wondering, anime is just animated pictures, similar to American cartoons, though of higher quality and for all ages. Manga is similar to comic books, but in japan manga is widely accepted and read by all ages.

The four cases

  1. Anime derived from Manga - An example of this is Trigun. (The manga is two series but there is only one season of anime) This is where the crucial choice comes in. In 99 percent of the time, the manga will be more in-depth, and better to read. There is a chance the anime is worth it because it has different parts that are worth seeing. Quite a few animes expand on the manga, though more cut out scenes. If you have a friend who knows more about the mangas you can always ask which the creator calls the "official" version. It's really up to if you want the "real" version, or do you want the one you will enjoy the most.
  2. Manga from anime - This is quite rare as the only one I am aware of is Neon Genesis Evangelion. A wonderful anime, but the book is considered quite better for hard core fans. I personally don't understand why this would be done, but it does happen. The manga again may be less then the original anime. In this case the Anime tends to be better for first time viewers.
  3. Anime from other sources (games) - Such as Arc the lad. The manga and the anime can go in either order, it really doesn't matter, I find these to be mostly "tie in" and not even worth watching. Most of these cross overs (including Street Fighter, Mortal Kombat) are action based and while manga does a good job with action sometimes, the anime is the way to go. The quality of both though tend to be awful as they are trying to squirm more money out of "stupid" fans, see the American example George Lucas 1977-present. There are however a very select few series that are worth watching that come from other sources, in this case it is usually the anime that exists if anything. Each case however is different. (Two more examples are Star Ocean, and Rockman.EXE) If at all possible just go with the original source.
  4. Manga continuations - An example of this is the Cowboy Bebop manga, while it is not technically a sequel (for the obvious reason in episode 26 of the anime) it is a continuation to add to the story of the crew. These should be a no brainier, the anime is always better as they set the story, but the manga has merits and can be read after finishing the series.

One thing to think of, if you want to translate it yourself, ask yourself, "Do I want to be able to go at my own pace or do I want to have more graphical context?"

Otherwise, you will also need to worry about how good the translation groups are, there are seen some truly worthless translations, not just one or two.

Finally forget everything written here, it is really up to the person. There are people who don't want to read, because they are that lazy. There are people who want the authoritive version and won't care about which version it is. There are people who will get both types because they are willing to blow 200 bucks just to get the full story.

The moral? The choice is up to you. If you enjoy doing it your way do it, we all don't have to be the same. The reason they have both versions is because people have different preferences.

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