Too many people hail the shotgun as the ultimate zombie killing weapon, often claiming that it's easier to get a hit because more pellets land on target, and guaranteed organ shreddage from all the shots yada yada. It's not that hard to simply
practice with a weapon until missing an undefending target running
straight at you from several meters is near impossible. That aside, the spread of shot isn't as wide as a lot of people would like to believe, the benefit of a reduced need to aim is negligeable and if you tamper with the shotgun to widen the dispersal you lose stopping power as less shot lands on target. Anyone hip firing a shotgun is begging to waste shells anyway, aiming is just
smart
The shotgun also has a much shorter range than an assault rifle. They make assault rifles in calibers that can drop a human target from the inertial transference alone (apparently?). A headshot typically kills what most people view as a zombie and even if you don't go for a headshot, a single 45 caliber tumbling round is going shred the internal fleshy bits and pieces of a target to ribbons. It'll do just about as much muscle tissue and bone damage as a shotgun if not more. Then there's the occasional military, swat, or cop zombie wearing protective gear when he died. Pistols and Shotguns are going to SUCK against them.
Semi-automatic shotguns can fire as fast as you can pull the trigger, full-auto weapons fire 15-20 rounds a second (though if you're surrounded by zombies and doing the ol' spray and pray you'll likely die). Fully reloading a shotgun is also much slower than reloading a magazine. I'd much rather handle zombies at range. The logical choice then is a large caliber assault rifle with an extended magazine of some kind.
That said, A12! With Frag shells!