The main advantage of public transport is that benefits the environment. A train or bus can carry far more people than a single car, using only one tank of gas / energy source in the process. Lots of trains and trams run on electricity which reduces the effect of carbon emissions even further. Until the electric car becomes more common, public transport will always be the greener option.
You also do not have to worry about finding a place to park, or filling up with gas, as you would if you were in your own vehicle. On the other hand, the advantage of taking your own car is that you will never have to wait for your train, tram or bus or share your travelling experience with members of the general public.
Another advantage of public transport is that it decreases the level of traffic on our highways making journey times quicker and the roads less crowded. Because of this, the possibility of an accident occurring is lessened, thus making public transport an overall safer option.
The main advantages of private transport are that it allows you to travel at your own convenience. You are not held to the constraints of scheduling, or the necessity to interrupt your journey with extra 'stops'; you can travel how you want, where you want, when you want, with who you want, while carrying and using what you want.
However, using private transport is far more costly than its public counterpart. Not only do you have to continually fill your tank with gas, but you also have to pay the tax, insurance and maintenance of your vehicle, not to mention the purchase price itself.