As a student currently at a university going into front end design, I think either approach can work well so long as you're willing to work hard and do more than is required of you.
If you can find a willing and good teacher and are also willing to start with little pay, working from the very bottom up, going straight into the business is not a bad decision. You'll learn what you need to know and get better at doing your job over time. The information you'll learn will be very, very practical. This way you won't have to pay tuition and you'll be doing exactly what it is you think you want to be doing. The potential problem is that many places would not hire you in the first place, you'll have to have some work or portfolio already to show them in order to be considered for the position.
On the other hand there are several advantages to going to a university. It forces you to build up your portfolio, gives you a more general education, allows you to take a look at other fields and perhaps change what you want to do in life, let's you start "real work" later on in life which allows for more freedom, gives you connections with the academic community as well as the pool of people around you, and potentially gives you more free time to work on what you want to do. The only real downsides I can think of for it include paying for it while not making much money and (debatably) holding off on going directly into the field you think you want to be in.
Either way, you should be reading and practicing outside of whatever it is you're doing to make yourself more valuable and stand out from the others. Real experience doesn't come from school or being taught by someone, it comes from actually doing something.