The obvious reason why War and Peace is usually described as a novel and not as an epic is that verse is one of the defining characteristics of the epic. Applying the descriptor "epic" to novels is a relatively recent phenomenon in the history of literature. Since the question cites Britannica in support of the claim that War and Peace is an epic, let us look at the beginning of that Britannica article:
long narrative poem recounting heroic deeds, although the term has also been loosely used to describe novels, such as Leo Tolstoy’s War and Peace, and motion pictures, such as Sergey Eisenstein’s Ivan the Terrible. In literary usage, the term encompasses both oral and written compositions.
The remainder of the article discusses characteristics and examples of epic poetry, rather than novels, although the author points out that (emphasis mine),
Novels and long narrative poems written by such major authors as Sir Walter Scott, Lord Byron, Alfred, Lord Tennyson, William Morris, and Herman Melville were patterned, to some extent, on the epic. Their fidelity to the genre, however, is found primarily in their large scope and their roots in a national soil; their distance from the traditional oral epic tends to be considerable.
Cuddon's dictionary of literary terms presents the following definition:
An epic is a loong narrative poem, on a grand scale, about the deeds of warriors and heroes. It is a polygonal, 'heroic' story incorporating myth, legend, folk tale and history. Epics are often of national significance in the sense that they embody the history and aspirations of a nation in a lofty or grandiose manner.
Cuddon's seven-and-a-half page article about the epic discusses many examples, moving from the Sumerian Gilgamesh to the 1960s. At the end of the article, he points out that,
In the last hundred years or more the novel, the cinema and, to a lesser extent, the theatre have been much favoured media for narratives on an epic scale. In retrospect it seems fairly logical that as the novel developed so the novelist would find it an increasingly suitable vehicle for a grandiose treatment of individual and national destiny. Indeed, there has been an impressive number of novels which can fairly be described as epic in their range and magnitude.
The examples Cuddon gives include War and Peace, Finnegans Wake and Dr Zhivago. Note that Cuddon writes "described as epic" (i.e. using the adjective "epic"), not "... as epics" (using the noun); these novels are like an epic rather than epics in the original sense of the word.
Chris Baldick defines the epic as follows:
a long narrative poem celebrating the great deeds of one or more legendary heroes, in a grand ceremonious style.
At the end of the entry, Baldicks adds,
The action of epics takes plae on a grand scale, and in this sense the term has sometimes been extended to long romances, to ambitious historiical novels like Tolstoy's War and Peace (1863–9), and to some large-scale film productions on heroic or historical subjects.
In Dutch, the term epos is a synonym for "heldendicht", which literally means "poem about a hero or heroes". The entry for "epos" in dbnl's lexicon for literary terms does not even mention novels or any other genres that are not written in verse.
Conclusion: Strictly speaking, the epic is written in verse, whereas War and Peace is not. From this perspective, the novel is like an epic due to the grandiose scale of its action, not an epic per se.
References:
- Atsuhiko Yoshida: Epic. Britannica.
- Baldick, Chris: The Concise Oxford Dictionary of Literary Terms. Second edition. Oxford University Press, 2001.
- Cuddon, J. A.: The Penguin Dictionary of Literary Terms and Literary Theory. Third edition. Penguin 1992.
- dbnl: Algemeen letterkundig lexicon (containing 4,600 terms, in Dutch).