Using an empty bar allows you to work through slightly more range of motion than an ab wheel. The bar sits a little lower to the ground which means your body can fall flatter.
This will also place the points of contact (the bar and your knees, or feet if you're doing them standing) further apart. The further the distance between these contact points, the harder your abs must work to keep your lumbo-pelvic region positioned correctly.
The most underutilized pieces of equipment in most gyms are the dumbbells. Oh sure, you might see people pumping out a few sets of biceps curls, bench presses, or flyes, but in most gyms the dumbbell racks are primarily used as a place to lean against between sets of barbell squats or benches.
This article isn't going to overwhelm you with neuroscience or obscure language. Nope, it's going to be bare-bones simple. As I've learned over the years, elementary advice is usually what helps people most, and it tends to work best.