I recently got back from a 16,000km road trip in my camper van across Northern Canada and Alaska for about 5 months, but prior to that I have hitched every trip that I've ever embarked on. Obviously both options have their pros and cons, but it really just gets down to what kind of trip you want to have. The vehicle provides an immediate sense of protection from the elements that is hard to attain from sleeping under a bridge in a rain storm. You will also have access to more isolated and far away spots, because face it, walking 100km down an old forsaken road to nowhere with your pack and your dog may sound romantic, but its a hell of a trek. Gas just plain sucks, so if you plan on moving around a lot you should also plan on spending hundreds, if not thousands of dollars. All that being said, hitching is an adventure all in itself. The weather can be a problem sometimes, especially if you're suddenly stuck in an area with high amounts of rainfall every day, but personally I would vouch that the pros outweigh the cons. Usually you'll have to wait a few hours for a lift, but as long as you've got your old trusty harmonica or set of juggling balls, it'll be fine. For me, the point of travelling is to meet locals and share new experiences with them that you couldn't find at home, and while hitching you are going to do all that and more. Car travel can really cut you off from other people, and unless you are purposely seeking out other travellers to be with, you might not find any.
To sum it up, I suggest a good ole' fashioned hitch.