You can get some of this info from the UIUC site… I think they go through the required classes (which for CS I believe are the same–it’s the other classes that differ when you are in LAS, which of course is easier to get into as well).
This board has been really, really quiet --you might get a more informed response if you post on the math/CS majors board.
CS+Stats in LAS and CS in ENG go through identical core CS curriculum. CS in ENG students generally take more CS tech electives (more are required and there is more room for them in the schedule as they are not taking those extra Stats classes).
LAS and ENG have different core requirements (foreign lang, physics, chem, etc). These are easily found on the school website if you need details (most successful applicants AP out of many of these requirements anyhow, making the impact of differences minimal). CS+Stats majors have access to essentially everything offered to CS in ENG students from the CS department. The ENG-specific study abroad program (IPENG) is one of the few things a CS+Stats major would not have access to. CS+Stats students have access to all career services/fairs, facilities, etc. that a CS in ENG student would have.
Which is a better idea? Impossible to say which is better for you. School claims no discernible difference in outcomes. I imagine, as with most things, your performance and skills developed will play a much larger roll in outcomes than which major you graduate with.
CS+Stats vs CS major in ENG with a Stats minor seems like a distinction without a difference to me.
You are still applying directly to a major, so it’s not like Berkeley (or, if I recall correctly, Michigan) where you simply need to be competitive with the others applying to that College. At those schools, there is a noticeable difference in selectivity between CS in Engineering vs general admission to L&S or LSA.
At Illinois, the CS majors in LAS get far fewer 1st choice applicants, but they get a ton of 2nd choice applicants from those who are rejected by CS in ENG. so the stats for those accepted to the CS majors in LAS are only slightly lower on average (this has been confirmed by the dept, although in vague terms and not with actual #s). Might depend on which of the CS+X majors get the most apps in a given year.