Personally, it would matter on the setting to me. If we are in an informal setting or just out and about I think it's cute when a man introduces his wife as his bride. It makes one think of newlyweds and just lovey dovey-ness. In a business setting though, I would prefer to be addressed and introduced as a wife. I think it delineates a bit of respect and permanence, like you two have weathered a lot together and are in it for the long run.
On a side note, when someone introduces their wife or husband, I think it's more appropriate to introduce someone as "Jessica, my wife" as opposed to "My wife, Jessica." To me it's like saying "this is someone important to me who has a name and how they are significant to me" as opposed to "here is my property, she has a name."