As you've obviously figured out, there isn't a whole lot of difference between the two routes.

Judy is right in the sense that your biggest problems in a speed run like this is getting stuck in city traffic.

Because of that, I think I would lean towards the Rockford, St. Louis, OK City route. You might hit a few problems in St. Louis, but I wouldn't see too many other problems this way. The downside is that it does have more tolls, including a brief stretch in Illinois and a large part of the drive in Oklahoma, and it might have a little more overall traffic as it follows the basic path of Route 66, and still gets a lot of California-Bound Traffic.

The other route (Chicago, West of Memphis, Little Rock) wouldn't have as much traffic except for Chicago, and wouldn't have any other toll sections outside of Chicago. However, Chicago traffic, as you probably know, can be a nightmare, even if you avoid the downtown area. Because of that, I personally would likely take the other route.