BA household and Qatara Family, while intending to do similar things, do it very differently.
BA household accumulates points on individual FF number. Each gets status, etc., along with AVIOS. Redemption uses points proportionately from all accounts.

Qatar—You can have a Single main account, and you add others as Avios accumulators only. Family members' Avios are added to the main account holder's. Family members do not get any benefits.
This is great for adding kids and older parents who do not travel much to let main account holder get avios with little hassle.

We have a BA household, Qatar individuals for adults, and added kids and rarely travelling parents on one of the Qatar accounts as family members.

BA program is better in most aspects. The only advantage Qatar has is that you do not need a separate email address, password, and account for Qatar FF for family members. It's simple, specifically for kids and family members who travel rarely but travel on Qatar/One World. We use this for kids and our parents to pool in one spouse's main account.

We usually end up moving all Avios to the BA household, generally for partner booking, etc.