So I can't comment personally on either of these books since I haven't read them, but I did do a quick search on the Academic Research Database JSTOR to check what peer reviewed articles said about "A History of Christianity." Here are some excerpts:

"Many readers will be offended by the condescendingly simplistic, inappropriately colloquial and annoyingly careless style of the book... Errors of substance, too, can be found. In the discussion of the Donation of Constantine the dependency of that forged document on the the Actus S. Silversti is not acknowledged, furthermore, it is mysteriously identified as "a document... in the legal texts of France" and erroneously assigned to the first half of the nine century rather than to the second half of the eight century (p58)... In general, then, this book is a disappointment.

Chadwick, Owen. A History of Christianity Review, The Catholic Historical Review, Vol. 83, No. 2 (Apr., 1997), pp. 281-282

There were two other peer-reviewed articles which I skimmed and they both had issues with the book as well.

Early Christian history is such a complex topic, and the issue is that since for the majority of the last 1,500 years, the majority of the people in the west have been Christian, thus many think they are experts on it because they have read their bibles.

Books for general audiences that are significantly better (IMO) and better respected in the scholarly community are: Crossan, John Dominic: The Birth of Christianity : Discovering What Happened in the Years Immediately After the Execution of Jesus or Ehrman, Bart: Lost Christianities: The Battles for Scripture and the Faiths We Never Knew

Not familiar with him, however as a general rule one should take any history book with a grain of salt. People will always inject their opinions, unknowingly even, into work they produce.

Johnson is a journalist rather than a historian. He writes about a huge range of subjects and isn't an expert in any of them. He began as a leftist but shifted to conservative Catholicism in the 1970s. He is very readable but he uses his books to make a case (usually attacking modernism) rather than to examine the evidence. He is not reliable but he can be entertaining and provocative.