Where to study is a very personal decision, but I can think of some important differences between both.
Studying in your local school or university will add lesser new things to your life: you will still live with your parents, same friends nearby, same shops and cafes, etc. So you can only focus on studying. This is great if you tend to get stressed by changes. Staying at home in a familiar environment will make you feel safer. You could even get a job on the weekends, and save some money for the summer.
On the other hand, moving to a different city or country will definitely introduce you to new things, that, of course, will add to your life knowledge on top of the academics, but could also take you away from studying all day. You will have to manage your time to go shopping for food, cook, clean your room, do laundry, etc. Living on your own means multitasking every day, all day long. This improves your organizational skills a lot!
At the end of the day, it is your decision and it will be fine either way, just try to take the time to think of every aspect of each option before you set your mind to it! What other differences can you think about going away to study or staying at home?