My lot lived in a playhouse for 5 years and were very happy. They are now in a 6X4 shed which they seem to like even more, it's easier to clean out too.
I would say that if you have a very small garden, playhouses are less imposing and if you're short like I am, you can find ones that will let you stand up.
However, if you have the space, sheds are much easier and you will get more for your money.