It is possible to open your bite and correct the occlusion with orthodontic treatment. However, to do so, your age and gum strength should support. If your dentist recommends you for braces, I believe, your gums and other supporting structure are pretty strong to accept the procedure. With the help of braces, it is possible to realign tooth position to the desired need and in general, it would take upto one year of treatment duration. Your condition is called " deep bite " which tend to damage the lower front teeth on due course of time if left unheard. It's better to opt for orthodontic management rather than the crown because of two reasons. 1) unnecessary grinding of tooth structure which is not a conservative procedure. 2) Even after placing the crown, there are more chances for the prosthesis to abrade or become wear-off because of minimal space available in your condition. For these reasons, it is better to go for braces, providing that your gums are supportive. I hope this helps to decide better.