Already some good angles from Patrick,
I would go for the redirect as Patrick mentioned above, but there's one particular situation in which I would keep both sites, and that's if you're using another proposition for your products/services.
Let's say you sell sunscreen, and one is completely focused on sunscreen to protect the skin of your children, while the other one focuses on sunscreen to have a nice tan. Maybe a stupid example but I hope you know what I mean.
There are many situations in which people are looking for other stuff (or use other keywords/search terms) but at the end just need the same solution (in this case Sun Screen).
Pro of using both sites: you can get more targeted traffic and really focus the proposition on those people.
Con: you have 2 websites which you need to market, which can cost you more time (and money).


says another Belgian.