By Object Browser, I assume you mean the Managed Object Browser(MOB) interface. They are different in both their scope and functionality although you can probably get similar information. Please see this MOB article for further information - http://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=1017126.
You should be able to see the differences when you use both interfaces. The Datastore browser either via vCenter or individual Host, is looking specifically at the file level objects in a "Windows Explorer" type GUI, of the Datastores.
The MOB is looking at various elements of the vSphere environment and "invoking methods" to retrieve the information.