As mentioned in other answers, there are size and lifespan differences you might want to consider as well. Obviously a bigger snake needs more space.
As far as difference goes, it's all dependant on the snake, and the previous owner. Some snakes can just be totally against handling, and there's nothing the owner can do about it. Generally, you'll find snakes with those personalities to be the species that are newer to the pet industry, so most king snakes and some boas should be generally easy to handle. Just know their are always exceptions.
When you get a baby snake, it's all dependent on you to handle it regularly. Regular handling while the snake is young is what gets the snake used to human interaction - giving it the friendly personality. A snake that is rarely handled is more likely to avoid human interaction, and even strike at hands that enter it's cage because it still feels that humans are dangerous.
So when you get an adult snake, you can get the advantage of a snake that's already been handled regularly. Giving you a head start (you only have to get it used to how you smell), and a more mellow snake. But, you have to be wary of people selling snakes they've had as pets, because they're selling them for a reason. Maybe because they found that caring for the snake is too expensive, or having a snake as a pet isn't what they first imagined it would be like, or more importantly to you, they didn't have time for the snake.
I would say adopting an adult snake from someone is more of a rescue operation, and if you take on the responsibility, you should be prepared for a snake that might need some extra attention. Getting it settled into it's new home, and possibly some type of re-taming.