There is a third way!
You could always set up a joint account to cover the main household bills, then have your own separate current accounts for your personal expenditure.
That way you can budget effectively by making sure there's enough money to cover the bills each month and have your own money to play with, rather than rely on "housekeeping"!
You might also be able to set up these current accounts with the same bank thus making it quick/easy to transfer funds between them if you need to.
With regards to savings, it's a case of trust and tax!
It does make sense to have savings accounts in the name of the person who isn't paying tax. But, you've got to be able to trust them! But, if you're having a baby together, then you've got to sort of trust each other anyway haven't you.
Personally I just went straight for the joint current account. Makes life a lot simpler as you don't have to transfer money to and fro and worry that you're other half might get stuck without any money. Does take a while to get used to "sharing" the current account, but does also force you to be more careful with your money as it can be easy to forget that someone else is also spending money when you come to budget. But, if you set yourself a weekly cash allowance that you withdraw at the begining of each week, it's quite easy really.
Good luck!