For vectors, you can edit the feature directly in ArcGIS and those edits be reflected in the layer online. Its simple. After you have your published service running in AGOL, open ArcGIS (10.1) (**NOTE - the feature layer must be enabled for edits). Using the Add Data button, select to "Add Data from AGOL. Make sure you login to your AGOL account.
Find the data you want to update or edit, and click "add".
Next, right click on the top level of the layer (see attached) and select Edit Features -> Create Local Copy for editing.
Make your edits / changes, and then do the same procedure as above, except this time select "Synchronize Local Edits with Server"
I use this a lot, and is easier than having to "overwrite" services, which does not seem to work, as many posters above have indicated.
-Z