You do not need to keep both in your kitchen, but it sure helps. All-Purpose is the workhorse; Self-Rising is the weekend helper. If you are a confident baker, All-Purpose gives you freedom. If you just want a quick biscuit with your coffee, Self-Rising is your gentle hug.
I keep both in my pantry, but I label them with a marker because I have grabbed the wrong bag more times than I care to admit. And you know what? That squished pancake-tortilla hybrid was still pretty good, because flour is forgiving like that.
The real difference isn’t about being “better.” It’s about knowing who does what job. Choose your flour like you choose a tool from a drawer: the right one makes your life easier, and the wrong one makes you laugh later. So go bake something simple, and don’t overthink it. Your kitchen is for joy, not for exams.