the actual differences may depend on the specifics of the O/R technology you are using.
When using JPA or Hbernate two differences which come to mind quickly are that it's all or nothing - if you choose field based persistence usually ALL fields are managed (by default), if you choose to use property based persistence all property accessors are persisted (by default). Depending on the interals (fields) and externals (properties) of your class it may be easier to use one or the other.
Another more important difference is that a getter/setter method can do more than just setting or getting a field value. If this makes sense for the application in question it may be better to use property based persistence.