Done a bit of research and I think you are in Holland (it would be really useful if you created a Mumsnet Profile and put your country info on it, then people wouldn't have to ask or assume). Therefore, immigration and work rules I can't help with - so will just say that you need to check that whoever you employ is entitled to stay/live and work in the country. You will also need to check how taxation, social security, pension, medical care that sort of thing applies to employing a nanny.
I will assume that you are meaning that you will be at home at the same time as the nanny:
Pro: you get to spend more 1:1 time with each child, as nanny can spend 1:1 time with the other child.
Pro: you can have someone else cook lunch, whilst you spend time with your children.
Pro: you can go out and leave your children at home.
Con: you have someone else in your home making it messy, getting in the way.
Con: children don't know who is in charge, may play each adult off against each other. This can be overcome by having it clear as to who is in charge at what point... and adults backing each other up (even if they don't agree at the time).
Con: Things get moved by nanny, may not put things back in the same place as you would. Nice to have someone else do the washing up, not so nice when you spend time hunting out your favourite mug.
Con: You can't walk around the house in your PJ's (or worse). Well you can I suppose but you need to not worry about what your nanny might think.