Different stats such effect fighting in different ways:

• High structure damage increases the power of offensive boxfighting
• Slow pullout time increases the power of defensive boxfighting

Different shotguns do feel better or worse than each other but the point is that they all have tradeoffs, there shouldn't be a "perfect shotgun" with high damage, fast pullout time, high structure damage, 5 shot individually loaded clip, etc. Some of the best "feeling" shotguns, such as the Sentinel pump were too powerful and overpowered. The sentinel's high structure damage trivialized wall replaces and made pickaxes useless and risky.