I've touched Russell's history, but that was quite some time ago. I would recommend Adamson over Russell, if only for being more approachable. But in addition to that, Wikipedia's article on Russell's history mentions that it's quite polemic on the ancient philosophers. I do recall not being satisfied with Russell's treatment of the atomists (Democritus, etc.), so I've just had a look at it again:
Adamson contextualizes the atomists (who content that there are indivisible particles) as a reaction against Zeno and his paradox, which seems very plausible.
On the other hand, before he discusses how the atomists might be reacting to their forebears, Russell says
> The atomists, unlike Socrates, Plato, and Aristotle, sought to explain the world without introducing the notion of purpose or final cause"
But what use is comparing the atomists against the later thinkers? Russell seems to have an interest in showing the superiority of a mechanistic view of the world.
> The atomists asked the mechanistic question, and gave a mechanistic answer. Their successors, until the Renaissance, were more interested in the teleological question, and thus led science up a blind alley.
> In regard to both questions alike, there is a limitation which is often ignored, both in popular thought and in philosophy. Neither question can be asked intelligibly about reality as a whole (including God), but only about parts of it. As regards the teleological explanation, it usually arrives, before long, at a Creator, or at least an Artificer, whose purposes are realized in the course of nature. But if a man is so obstinately teleological as to continue to ask what purpose is served by the Creator, it becomes obvious that his question is impious. It is, moreover, unmeaning, since, to make it significant, we should have to suppose the Creator created by some super-Creator whose purposes He served. The conception of purpose, therefore, is only applicable within reality, not to reality as a whole.
So you can see how Russell has as part of his aim trying to share his own views and judge these earlier thinkers with some hindsight. On the other hand, Adamson is primarily trying to interpret these authors and speculate and relate how they might have arrived at the conclusions they might have arrived at. I've not read Adamson beyond the Classical Philosophy volume, so I hope that the quality remains just as good.