As someone who used to hire CS grads and my husband continues to do so, there is a big difference in the actual comp sci degrees at these 2 schools as mentioned by others above. You may want to look at the options and required course work side by side. My DH has a BA in comp sci (and linguistics) and a MS in software engineering. I have a BS in comp sci and a BS in math. We were doing the same job at the same pay level for a while. And I’m not saying one is better than the other. Our BA CS grads tended to be hired for different things than those with deeper tech education. I actually think I would have enjoyed a BA program much more but my college options were severely limited by my parents. And it had nothing to do with school name at all. We knew which programs were the most technically rigorous. Many were state schools with engineering programs. I also think a BA program is better for someone who is more unsure about what direction they are heading.
That said if you are getting in state tuition for UW, that would be pretty compelling for me. If she wanted to stay another semester to cover more of another subject like creative writing it would still be cheaper and she’d have the more rigorous degree.