I have both, and I greatly prefer the child seat. It's locked to my bike so no need to secure, and I can talk to my DD the whole ride, and know when she needs a break. She even signals when I do - which is super cute. I found the stability issues to be mostly a problem getting on and off my bike and when stopping, once you are moving at almost any speed you won't even notice. I started out with a 25lb kettlebell strapped in the seat so I could figure out the balance - it took a few rides to be comfortable and some upper body strength is required. Now I don't even notice. I have an elongated rack and can easily carry a light diaper bag with the baby seat. However no groceries - they were too heavy and the bike was squirelly... I would need a front rack to balance the weight front to back and alas my front carbon fork is not rated to carry any weight at all.
We took the money I saved from bike commuting for a year, and splurged on a long tail cargo bike. It has a low 20" back wheel, so the center of gravity while carrying kids is much lower, and it has a double kick stand that is easy to kick up once you are on the bike. No stability concerns at all, and it fits 2 toddler seats or 3 preschoolers, and a load of groceries :). I wouldn't recommend it as mustachian - because a trailer is definitely the more economical option - but it is purpose built to haul kids and cargo - it is a joy to ride. We have only had 3 tanks of gas since last October - here's to half that this summer...