How are Mexico and US independence similar?

Answer 1

Both American and Mexican revolutions involved both sides seeking freedom and liberty. Both sought to expel or to get rid of European powers. Both side wanted the right to govern themselves. That's how both sides are similar.

Answer 2

Both independence wars were waged between colonists born in the Americas and the European authorities that tried to keep both colonies as part of their respective empires. In the case of the United States, the war was fought against British forces, while Mexico had to fight Spanish Royalists.

Besides that, everything else is different, including the reasons of such independence. For example, Americans were weary of paying taxes, while criollo Mexicans (people of European ancestry born in the Americas) saw the invasion of Spain by Napoleonic forces as the perfect pretext to break-up from Spain and rise to power on their own.