I would actually go to Arizona State online. Here’s why:
ASU, like many state schools that offer online programs, most likely offers the same degrees that they do for in-person students. Thus, I believe you obtain the exact same degree (though, of course, you will want to email them to verify that is the case for both your transcript and diploma).
Harvard Extension School is the continuing education wing of Harvard. It is NOT as prestigious as the “regular” divisions. Among the educated circle, most people know exactly what Harvard Extension School is and what is required to be admitted. I would NOT say it is more prestigious than the average state school whatsoever, and over the years, there have been people who have actually gotten into trouble by misrepresenting their degrees from HES as the traditional Harvard undergraduate degree.
This is a bit different from other non-traditional programs at other Ivies. For example, at Yale, Eli Whitney students receive the exact same degree and take the same courses. At UPenn, LPS students receive the same diploma (but their transcripts do note “LPS”). Harvard Extension School is not remotely like the rest of Harvard.