I was initially confused because I assumed that Krippendorff would take issue with Neuendorf's definition of content analysis but I wasn't sure why I thought that. Now I'm pretty sure that he's only criticizing far earlier definitions, although a little disingenuously. Check it out:
Neuendorf (2002): Content analysis is a summarizing, quantitative analysis of messages that relies on the scientific method … and is not limited as to the types of variables that may be measured or the context in which the messages are created or presented.
Krippendorff (2004): Content analysis is a research technique for making replicable and valid inferences from texts (or other meaningful matter) to the contexts of their use.
Exemplary older one:
Berelson (1952): Content analysis is a research technique for the objective, systematic, and quantitative description of the manifest content of communication.
Krippendorff takes big time issue with the idea that CA has to describe the "manifest content of communication." He claims that this definition of CA arises from the Shannon-Weaver model of communication which leads to the idea that one message has one and only one meaning. If we accept this model, then content is inherent in a text rather than acknowledging that multiple readings of a text are possible (i.e. there is a multiplicity of "content" and thus meanings associated with a message/text, depending on context - K's favored view, which is just constructivist?). If we take Berleson's definition (according to Krippendorff) then we have to accept the idea that the only thing we can content analyze is that which is the same for the sender, receiver, and content analyst (which would obviously be extremely limiting and boring).
Now, I think this is a bit of a straw man, since the early content analysts probably wouldn't agree with Krippendorff's description of what they were doing. If K is right, though, then he would have a point. I'm just not sure I can justify the expense of intellectual energy right now to dig deeper.
In any case, it seems that Neuendorf's definition is consistent with Krippendorff's since she has the idea of context, and says that any variables are possible (i.e. from extremely manifest to extremely latent). The idea of inference is also interesting -- apparently early content analysts (Olsti) wanted to be able to make inferences from the CA results to characteristics of the source or effects on the receiver. Krippendorff and Neuendorf are both fine with this in principle, but they want us to have more information about the source/audience for corroboration (which I'm in total agreement with).
At root it seems like K is just trying to inject some constructivism into this positivist model of CA from the 50's (this is a pretty tired debate by now, I'm sure...?). Neuendorf seems to acknowledge this also, but her exposition is a lot clearer than K's (in my opinion).