I also found a useful thread on Reddit (https://www.reddit.com/r/MBA/comments/eoxh2j/imba_illinois_online_mba_vs_boston_university/) and can add a few comments from speaking with applicants who have studied in or considered those degrees.
1. prestige. Both are huge, impressive powerhouses. US News gives BU a slight edge over UIUC, but Illinois has a much bigger scale. UIUC's scale means it performs better in most rankings. I think BU's status as a private university gives it a bit more glamour.
2. faculty quality. In terms of research citations, These two schools are more or less in line with scale - 285 faculty versus 235: https://jindal.utdallas.edu/the-utd-top-100-business-school-research-rankings/worldRankings#20152019
3. curriculum value. There's a 60% lead for UIUC: 72 credit hours of study versus 45 at BU. This is because BU has only the core curriculum, while UIUC also includes specializations courses and specialized capstone courses. This offers substantial extra value for people who want especially deep skills in any of its four focus areas: global business; entrepreneurship and innovation; digital marketing; or business analytics. However, if you just want the core curriculum, BU might save you time.
4. flexibility. BU is notably more flexible. It can be completed over six years, so as few as one 7.5 credit hour course per year. UIUC requires students to complete within three years, generally, that will mean at least 27 credits per year.