Creating or Using Existing Mythologies
Rick Riordan. When you hear that name, the word "demigod" or "magician" is sure to follow in your brain. This is because he's become famous for integrating the Greek, Roman, Egyptian, and Norse mythologies into the modern world.
There's something about mythologies that is automatically compelling for us. Mythologies establish a universe and provide explanation for why things are. We can chose to do as Riordan did and adapt an existing historical mythology or create our own like J.R.R. Tolkien did with Middle-Earth.
Using an Existing Mythology
Pros of Using an Existing Mythology: You already have a language, history, and deities to work off of. Riordan only needed to add and/or adapt the personalities of his deities and mythologies to make them fit in the modern world. You also can rely on most people knowing who is who in the mythology.
Cons of Using an Existing Mythology: What you chose to include/exclude and how you present your mythology says much more about you than it. For instance, Norse mythology is primarily about war and honor in battle. The Magnus Chase books focus very little on this. In other words, because you're using an existing mythos, you'll be judged on how you present it. Do it wrong by getting your facts wrong or presenting the mythology in an inconsistent way which leads to less sales and well deserved ridicule.
Creating your Own Mythology
Pros of Making Your Own Mythology: You have full control and can make your mythology be whatever you wish. Also, people are more interested in mythologies that aren't already existing ones, simply because they're new. It's also fun to make them. You can make new powers and deities that people will want to know more about.
Cons of Making Your Own Mythology: You have full control and it's wholly your responsibility to make the rules in your mythology consistent. Definitely write out the mythology and rules of your world and have other people look at it to make sure that you have everything consistent.
Personally I'm okay with making my own mythologies, but you're free to do whatever you wish. If you can rely on someone to edit or readover your books, all the better to do your own mythology. If you have time to do all the research into Greek or Norse mythology, and really want to adapt one of them, focus on that.
Farewell for now!