At Arkansas, Petrino had them go 10-2 through the regular season (lost to 'bama by just 4 points) in 2010. They followed that up with another 10-2 season in 2011 under Petrino. However, after that, the scandal surrounding Petrino broke out ... and John L. Smith took over for the 2012 season [maybe akin to an interim coach?] ... and the Razorbacks had a down year, going 4-8. Then, following that, they hired Brett.
Thus, given that Arkansas was just 1 year removed from 2 consecutive 10 to 10+ win seasons ... that points to Brett entering a pretty decent situation there.
In contrast, here is the time series of the Illini program under Lovie Smith:
'16: 3-9
'17: 2-10
'18: 4-8
'19: 6-7 (got a bowl showing!)
'20: 2-6
One of the big criticisms that Illini fans had for the program under Smith was that they accused him of being a "lazy" recruiter. That was certainly an issue ... but arguably a bigger one was a lack of a true identity (on either side of the ball).
Without question, I'd say that Brett is entering a much tougher situation than he faced in EITHER of his prior head-coaching gigs.
However, he will offer the Illini an upgrade in recruiting [he's a pretty tenacious recruiter] ... AND he definitely has a vision for the identity of his teams too. I think that he'll have less problem trying to institute a midwestern blue-collar toughness/nastiness identity in Illinois than in Arkansas. The trouble with doing so in Arkansas is that kids there see the basketball on grass style to their west (in Texas) ... and all the track-speed in the rest of the SEC ... and so it might be a harder sell to promote a more "traditional" style of football there.
I don't know what to expect from Illinois ... but I do know that it is a tough gig.