I've found the NARA locations page but cannot seem to figure out if these locations all provide the same services or contain the same set of records. If I visit the NARA location in Los Angeles is as good as visiting the one in Washington, DC?
No, not all NARA (U.S. National Archives and Records Administration) locations are the same. On the NARA Locations page you can see (in small type) the "Available services" for the location. If you compare Washington D.C. to the Riverside location, you can see the former has a longer list.
The list just gives you the basic categories of services available, however. You'll want to see more detail about the location you're interested in. Clicking on "more information" under the services list will get you to an overview page for the location (e.g. for Riverside). On the left you will see a list of public services, and the most interesting is probably the "Genealogy" link. On that page you'll get a better idea of what you can access at that particular site.
This question (excellently answered in the specifics by @RobertShaw) highlights the extent to which we have come to expect (and to receive) ubiquitous access to digitised records.
It is important to realise that the overwhelming majority of records in many significant collections are still held as physical objects that can be located at only only place at any one time. While major archives can offer near-universal access to their indexes (derivative records), genealogists and family historians still need to travel to examine originals.
National repositories delight us by operating at multiple sites, and infuriate us by always storing the records we need somewhere other than near home!