As line break strength increases, so does line diameter and this can have a big effect on how lures are presented. Wired2Fish staffers visually demonstrate this through a simple on the water test that compares the rate of fall of the same 1/2-ounce jig and trailer. The variable is the differing 10-pound and 20-pound line (0.011'' and 0.017'' diameter respectively). The results are surprising -- a modest increase in line diameter drastically reduces fall rate.
The "so what" of this pertains to many fishing scenarios. Experienced anglers are aware that lure fall rate can have a big impact on success and fish preferences can change by the hour. Case in point, if you're fishing a bottom bait such as a football jig in deep water, it's often advantageous to use the lightest line possible -- your bait sinks faster and stays down better (smaller diameter line = less lift). Conversely, you may need the break resistance of 20-pound line over 15-pound when flipping and pitching heavy shallow cover. This may require increasing lure weight to maintain the desired fall rate. The simple takeaway is the importance of factoring line diameter along with lure weight when working to optimize a certain presentation.
Line diameter also has a big impact on horizontal presentations. Gerald Swindle explains and puts this into practice in this excellent Lake Guntersville crankbait video.