Comparing Language Model of two corpora
If I understand your question correctly (please comment if I don't), you want to compare the output text from two different language models. Therefore, I don't think you should worry too much about the language models themselves.

If I was you, I'd probably do a simple TFIDF analysis so that you can gain a better understanding of what terms are more prevalent in certain news outlets.

Take a look at scattertext, it allows you to create visualizations like the following: