Service Locator is just the lesser of two evils so to say. The “lesser” boiling down to these four differences (at least I can’t think of any others right now):
Single Responsibility Principle
Service Container does not violate Single Responsibility Principle like Singleton does. Singletons mix object creation and business logic, while the Service Container is strictly responsible for managing the object lifecycles of your application. In that regard Service Container is better.
Coupling
Singletons are usually hardcoded into your application due to the static method calls, which leads to tight coupled and hard to mock dependencies in your code. The SL on the other hand is just one class and it can be injected. So while all your classed will depend on it, at least it is a loosely coupled dependency. So unless you implemented the ServiceLocator as a Singleton itself, that’s somewhat better and also easier to test.
However, all classes using the ServiceLocator will now depend on the ServiceLocator, which is a form of coupling, too. This can be mitigated by using an interface for the ServiceLocator so you are not bound to a concrete ServiceLocator implementation but your classes will depend on the existence of some sort of Locator whereas not using a ServiceLocator at all increases reuse dramatically.
Hidden Dependencies
The problem of hiding dependencies very much exists forth though. When you just inject the locator to your consuming classes, you wont know any dependencies. But in contrast to the Singleton, the SL will usually instantiate all the dependencies needed behind the scenes. So when you fetch a Service, you dont end up like Misko Hevery in the CreditCard example, e.g. you dont have to instantiate all the depedencies of the dependencies by hand.
Fetching the dependencies from inside the instance is also violating Law of Demeter, which states that you should not dig into collaborators. An instance should only talk to its immediate collaborators. This is a problem with both Singleton and ServiceLocator.
Global State
The problem of Global State is also somewhat mitigated because when you instantiate a new Service Locator between tests all the previously created instances are deleted as well (unless you made the mistake and saved them in static attributes in the SL). That doesnt hold true for any global state in classes managed by the SL, of course.
Also see Fowler on Service Locator vs Dependency Injection for a much more in-depth discussion.
A note on your update and the linked article by Sebastian Bergmann on testing code that uses Singletons : Sebastian does, in no way, suggest that the proposed workaround makes using Singleons less of a problem. It is just one way to make code that otherwise would be impossible to test more testable. But it’s still problematic code. In fact, he explicitly notes: “Just Because You Can, Does Not Mean You Should”.