It all depends on the attitudes of those around you. If you have an instructor, or go to a school ran by someone who believes women have no business in an airplane, then it will obviously be more difficult. There aren't a lot of people like that, but you better believe they are out there. Knowing that, if you run into those people move on. There are plenty of women friendly schools and instructors out there. Check out the Ninety-nines, lots of good stuff.
As far as physically flying an airplane, you are at a SLIGHT disadvantage. Some airplanes are very heavy on the controls and require some upper body stregnth, females aren't built like males and for the most part don't have the same upper body stregnth. With newer airplains, and pretty much anything you would use for training, this is not an issue. You have a slight advantage also, your brain works different, and your thought processes tend to be more organized than a mans, so that is a small benefit. Looking at the big picture, you're just like any student, they ALL have their advantages and disadvantages.
As far as making a career out of flying, my first point is still true. There are people out there that won't hire you because you are a woman (you can replace woman with any minority you choose), sorry but it is a fact of life. The majority of people doing the hiring of pilots won't count that against you, in fact many employers would rather hire a minority, as long as you are qualified for the job and they like you as a person. Looking at the big picture, I'd say you are slightly better off than a man, all things being equal.
If you're just getting into flying, check out the EAA's website (eaa.org I believe) and look into the young eagles program if you are young enough. It gets you a free indroductory flight (most schools charge about $50 for that) and last I knew they had a deal for a free private pilot self study kit, that is easily $250. Look into it...