The main difference is that in Sweden you don't need to do any paperwork to claim it, it is automatic.
The thing with these kind of benefits is that the bureucracy involved in dispensing them often costs close (or more) than the money dispensed. The system is more efficient if you just let everyone have it. It is one of the core arguments of UBI vs Welfare.
In this case the benefit still counts as welfare, not UBI obviously. However since the dispensing of the benefit is so simple (registered with tax agency, which is required to have an ID) it carries the same argument. If UBI was a thing in Sweden it would work the exact same way sans a check for parent-child relationship.
Also the amount per child grows slightly with every child up to 4 I think.
[1] https://www.gov.uk/child-benefit