I guess I am more of a continuum concept type of mother. I think that any restraining device, be it a baby carrier, stroller or harness should be avoided for a toddler or child except where circumstances are such that you absolutely have to do it to ensure safety (or of course if if the child WANTS to be in it (for example, she is tired or just wants to relax or be held)). Otherwise, I do not believe in systematically putting ANY restraining device on a child. I let my DD walk with me. If circumstances demand that she be held or sit in a stroller, then she gets picked up or put in the stroller for that limited period of time (in our case, usually a few minutes). Otherwise, she walks with me. I think that the more you encourage your child to walk with you, the quicker he will learn to do just that.
In what circumstances you think you NEED to restrain is your call, based on the age and temperament of your child, how many other small children you have with you and the environment in which you are in.
While we do use a stroller for when safety requires it, I tend to think that forcing a child to sit in a stroller is probably the worst because then you are just teaching him that being carted around in chair is better than walking or running. Why would I want to teach my child to be lazy? At least with the leash or harness, he can walk.