It is also possible to setup them up with their own Apple ID, but still control how much they spend using iTunes Allowances or gift cards.
I suppose it depends on how mature they are and whether your tastes overlap enough to make it worth saving money. If they are mature enough that you trust them to pick their own music and apps, give them their own Apple ID, then using either the Allowance feature or Gift Cards, you can control how much they spend but leave them free to pick their own content (or buy gift cards for themselves out of their own pocket).
If they are still too young for that, leave them on you account and control what they get yourself.
If you share the same tastes and don't want to buy things twice, leave them on your account. How much you trust them with making purchases is up to you.