Freeman is a classicist/intellectual historian with a masterful command of the ancient sources. He really loves his Aristotle and the Ancient Greek scientific corpus.
This particular book, however, seems to be (1) overly influenced by Gibbon; and (2) unaware of the extent of scientific knowledge in Constantinople.
For example, Freeman is concerned that the greatest Christian intellectual, Augustine, is unable to actually read the sources in Hebrew or Greek, and that no one, until Aquinas, knows Aristotle. Obviously, that was not the case in Constantinople. That said, you'll probably learn a lot about certain points of fourth and fifth century history. However, if you want to get a better picture of intellectual history in this time period, including the parts of Europe that were still part of the Empire, you should read Colin Wells' Sailing from Byzantium: How a Lost Empire Shaped the World
. Wells is also a classicist, and, like Freeman, a great author.
FYI, Mark Edwards published a good review of Freeman's book in History Today
. I could PM it to you. In it, he points out some specific matters of disagreement, but, I think, really captures the ultimate contradiction in his final paragraph:
Most questionable, however, is the title. Freeman seems to subscribe to the erroneous syllogism that since tolerance is rational and paganism was tolerant, paganism itself was rational. The fallacy escapes detection because his exemplars of the 'Greek tradition' are always sober and empirical writers -- the ones whom Christian scribes thought fit to preserve -- and not the superstitious multitudes against whom they aimed their satires. Rome in any case oppressed the Christians -- a fact that is only mentioned here and there in the book, though measures of reprisal against the pagans after Constantine's accession furnish a theme for several chapters. If it is a crime to raze a temple, it must surely be a greater crime to throw the congregation to the lions, and of the half-dozen philosophers who triumphed over the ashes of the martyrs in the first three Christian centuries, Porphyry was the only one to be punished by the burning of his books. Augustine is rated lower than his contemporary Themistius, as though it were especially meritorious for a pagan to employ his education in making paraphrases of Aristotle and grooming ancient platitudes for the delectation of Christian autocrats. Although the eighteenth chapter carries the story of western Christendom from 395 to 640, barely four pages are given to the two centuries that followed the irruption of the barbarians--just enough to remind us that the title 'Pope' was not always the prerogative of one bishop (p. 309). Yet it was after all the Saxons, Franks and Goths who felled the Empire in the west, and it was only because they all came under the sway of the Roman pontiff that the language, law and literature of the classical epoch -- and with them the pagan testimony against Christians -- have survived.