You have to take care of a set of daily tasks to keep them happy and healthy. If you work, you'll have to send the child to daycare, which you don't have to do with a dog, but for me personally, there's some mental stress associated with leaving a dog home alone all day. Other than that, you can't just up and leave your house for longer than a work day without making arrangements for either kids or dogs. Naturally, there are certain kinds of vacations that you can't take with children, but in my experience, most people vastly overestimate how much time they'll actually spend travelling the world over the next decade or two.
Dogs have to be walked regularly enough that I don't think it's unreasonable to say that a lot of people will spend more time actively caring for their dog than they would caring for a child once the child is older than 5 or 6, at least when the child doesn't have a ridiculous amount of extracurriculars, though that's far from universal. Some kids are quite self-sufficient, though.
In my mind, the major thing that makes dogs less of a responsbility is that they don't live as long, but then no one ever just has one dog, they tend to string together 30 or 40 years of dogs, whereas kids are theoretically out of the house after 18 years.
Lest it be said that I must not have much experience with kids, I have 4 and have been a stay at home dad. It must also be said that I derive much more joy from interacting with my kids than I do from interacting with my pets so my whole perspective is certainly biased.
All in all, I think culture has instilled in us this fear that we'll ruin our children's lives if we just let them be children and that has made having children so much more daunting and intense and exhausting than I think it needs to be(though babies, I fear, will always be intense and exhausting).