According to Hubs (who is a carpenter), the cedar used for fencing is the "cheap stuff"- it is the heart wood that is highly aromatic and used for closets and such. We used it for fencing around our trash yard. I have to say that even brand new it was not aromatic. I think it would be fine, especially if you put some type of sealant on it.
Redwood, though rather pricey, is one of the best woods for an outdoor application as it resists rotting from damp weather.