This is really a personal choice, but here is my two cents about it.
Breeder: A good breeder will guarantee the health of your dog, which is part of why you pay so much for a dog from a good breeder ($500-$1500). You will also have a great resource just a phone call away if there are any problems or if you need any advise. You can visit the parents and maybe siblings to get a feel for what possible personality traits your dog may have. You can also talk to other people who have bought from that breeder to see how their dogs are doing.
Keep in mind that it is hard to find a truly reputable breeder. You may have to sign a contract that you will feed the dog something specific, train them with a specific trainer, neuter they by a specific age (or not at all). Also, there is no guarantee that your 'blank slate' puppy will grow up to be what you want him to be. Like people, each animal is unique. Just because a breed has specific traits does not mean your individual puppy will share those traits. You also will not know exactly how big your dog will get or what it will look like (you will have a pretty good idea, but genetics can be unpredictable). Along with your purchase price, you will have to come up with and additional $500 or so to get all the puppy shots and neuter done. You will also have to potty train a puppy, getting up every 2 hours to let it outside, even in the middle of the night. Plan to take 1-2 weeks off of work if you go this route.
Adopting: You will save a life first of all. You may also end up with a well bred purebred as about 25% of all shelter animals fall into that category. If you adopt from a foster based program, the foster family will have had time to learn all about the dog. This way, you have a better idea of what your dog's personality is. If you adopt an adult, you will take all the guess work out of how big he will get and what your dog will ultimately be like. Shelter dogs are cheaper ($100-$500) and have already had all their shots and been neutered. So there is no additional expense right away. Arguably, mix breeds are also healthier as they have less inbreeding. You also have complete control of what you will feed your dog and how you will care for it.
The down side is that you don't have a health guarantee, and the shelter workers may not be there in the future to help you with problems. A dog with an unknown background may have health or emotional issues you will have to deal with. You cannot compete in many dog shows and events, and cannot register a mutt. Most shelters only have a 2 week return policy, and very few will give you a refund. Usually it is an exchange.
Personally, I adopted a pure bred mastiff from my local animal control for $150. She is calm, potty trained, well mannered, friendly, good with kids, cats, dogs, everyone, and had all her shots. We had to teach her basic commands and spent about $1,000 to fix some medical issues. We don't know how old she is, but she has been a great fit for our family and we feel we made the right choice with her.
What ever you choose to do, good luck!