1. Iowa: 90-77 (.539) - A lot of bad blood in recent years and WAY more of that historically, ranging from the Bruce Pearl saga all the way back to having to suspend both the football and basketball series for several years due to fights. While we both have other rivalries and two very big non-conference series' with as much or more history (Illini/Mizzou and Iowa/Iowa State), something about a conference rivalry hits different ... and I would say the vast majority of both fan bases would name this as their biggest hoops rivalry right now. I went to the game last Saturday, and it was awesome, despite the loss.
2. Indiana: 91-95 (.489) - Two states that care A LOT about basketball (from high school on up) with a very close series historically. There have also been various periods where it has heated up in intensity (Bob Knight/Lou Henson public feuds and the Eric Gordon saga), but it's mostly just a good series between two fan bases that care about basketball quite a lot and are in close proximity to each other. As a funny side note, we both randomly had the same names for our football and basketball stadiums (Memorial Stadium and Assembly Hall) for years, lol...
3. Northwestern: 142-43 (.767) - Just chose this one so I could show the hilarious record, lol. In all seriousness, I am not a fan of "gatekeeping" rivalries, and I have no problem calling NU a rival. It is a similar dynamic to Georgia/Georgia Tech or Tennessee/Vanderbilt, though - tiny, elite private schools located IN their states' big cities but outnumbered like 10:1 for fans in their own backyard. It will just never have the same intensity as others due to how different the fan bases are, but it'll always deserve some recognition (just as the others examples I gave in Tennessee and Georgia).
There are a lot of other conference series' with a lot of history and where tempers have flared at certain points, but there is a big dropoff after the top three. A few notes:
Michigan: 92-85 (.519) - A lot of older fans hate them still because our 1989 Flyin' Illini team whooped Michigan twice and then lost to them in the Final Four ... and considering we are one of the best teams to never win the NC, that stung. The whole COVID pause in 2021 where we went 16-4 and they went 14-3 and were Big Ten champs based on winning percentage got people riled up, as well, and then Hunter Dickinson has been quite a loudmouth about us (and everyone else...) in recent years. However, I don't think it's ever elevated the series into clear "rivalry" status. JMO.
Purdue: 90-104 (.464) - As another poster mentioned, we are the closest campuses to each other and both love hoops, so it seems like it should be bigger. I don't know if it's a mutual dislike of Indiana, the Keady/Bruce Weber connection that was relevant for years or just that last year was really the first year both teams have been good at the same time in recent history (Illini were dominant from 2000 to 2006 while Purdue sucked, Purdue became really good in the late 2000s and most of the 2010s while we were awful and Purdue was kind of "meh" for the first couple years of Underwood bringing us back to respectability until last season).
Wisconsin: 116-89 (.565) - Given the Bears/Packers crossover, this one should be a lot bigger. Additionally, when I was growing up it was always Illinois, MSU and Wisconsin battling for the top spot, so you'd think something more heated would have developed.
Honorable mention to Maryland for completely and utterly owning us...