There is just no telling how many apps they will get for the CS+Astronomy major, and that will have a major impact on competitiveness. It is a new major though, so it is probably safe to say that it will be less competitive than CS in the COE. All of the new CS+X majors will be popular 2nd choice majors for students applying to CS in the COE though, so I don’t think you should expect it to be that much easier to get in.
You can start [url=<a href=“https://cs.illinois.edu/prospective-students/undergraduates/cs-degrees-offered/cs-x%5Dhere…%5B/url”>https://cs.illinois.edu/prospective-students/undergraduates/cs-degrees-offered/cs-x]here…[/url]
If you poke around you will notice the the CS part of CS+Astronomy is the same as the CS part of the core CS curriculum in the COE. There is no difference in campus resources either (you have access to all the facilities, career fairs etc. that you would have taking CS in the COE). The major difference is you will have core LAS College requirements (more humanities) instead of core COE requirements (chem, physics), and you will be taking several more Astronomy classes, obviously (instead of more CS classes, many of which you will still be able to take as electives).
Finally, the administration is looking at the feasibility of pulling out all these majors into a ‘College of Computer Science’, although it doesn’t look like they are moving very fast on that (they seem to talk about it at the CS Town Hall every year). Who knows though, in the end you may be graduating from the same College as the COE admits…