Question: I'm refactoring a class and adding a new dependency to it. The class is currently taking its existing dependencies in the constructor. So for consistency, I add the parameter to the constructor.  

Of course, there are a few subclasses plus even more for unit tests, so now I am playing the game of going around altering all the constructors to match, and it's taking ages.  

It makes me think that using properties with setters is a better way of getting dependencies. I don't think injected dependencies should be part of the interface to constructing an instance of a class. You add a dependency and now all your users (subclasses and anyone instantiating you directly) suddenly know about it. That feels like a break of encapsulation.

This doesn't seem to be the pattern with the existing code here, so I am looking to find out what the general consensus is, pros and cons of constructors versus properties. Is using property setters better?

Answer: 
Constructor injection does explicitly reveal the dependencies, making code more readable and less prone to unhandled run-time errors if arguments are checked in the constructor, but it really does come down to personal opinion, and the more you use DI the more you'll tend to sway back and forth one way or the other depending on the project. I personally have issues with code smells like constructors with a long list of arguments, and I feel that the consumer of an object should know the dependencies in order to use the object anyway, so this makes a case for using property injection. I don't like the implicit nature of property injection, but I find it more elegant, resulting in cleaner-looking code. But on the other hand, constructor injection does offer a higher degree of encapsulation, and in my experience I try to avoid default constructors, as they can have an ill effect on the integrity of the encapsulated data if one is not careful.

Choose injection by constructor or by property wisely based on your specific scenario. And don't feel that you have to use DI just because it seems necessary and it will prevent bad design and code smells. Sometimes it's not worth the effort to use a pattern if the effort and complexity outweighs the benefit. Keep it simple.
It depends on how you want to implement. 
I prefer constructor injection wherever I feel the values that go in to the implementation doesnt change often. Eg: If the compnay stragtegy is go with oracle server, I will configure my datsource values for a bean achiveing connections via constructor injection. 
Else, if my app is a product and chances it can connect to any db of the customer , I would implement such db configuration and multi brand implementation through setter injection. I have just taken an example but there are better ways of implementing the scenarios I mentioned above.