In more detail, it depends on many factors:
- Is your parents's objection to you going OOS based on tuition costs or do they have other reasons for wanting you to stay close to home?
- Where can you get scholarships OOS, and would you willingly go to those schools? Some of these can be quite prestigious. The guaranteed merit aid schools are generally not high-prestige, but some prestige schools do have competitive merit aid.
- Will your parents pick up any of the difference if you want to go to an OOS school that costs more?
- If not, are you willing to get a part-time job?
- What is your intended major, and intended post-graduate plan? For some paths (e.g. law school) the prestige of your undergraduate institution will be of minimal significance. For others (e.g. I want to be an elite Wall Street investment banker), prestige and network can be very significant.
- Would gaining admission to an honors program (such as Barrett at ASU) change your feelings about attending an in-state school?
To sum up, the decision is very much about you, your parents, your plans, and your circumstances. There’s no one size fits all answer.