Kreiri may be right in thinking this a gibe at de Crèvecoeur's wordiness; but I think Orwell is alluding to a different catchphrase:
what a tail (often what a long tail) our cat’s got! A mid C19–20 proletarian c.p. at a female ‘flaunting in a new dress’, the rear skirt of which she swings haughtily or provocatively. (Ware: the shorter, the orig., form.)
Later it could be used of either sex and be addressed to—or at—a person boasting vaingloriously: usu. in the longer form. Leechman vouches for its Can. usage.
But Simon Levene writes, 1979, to correct my dating: he cites Henry Carey, The Dragon of Wantley, 1738, at Act II, line 43: ‘Lauk! What a monstrous tail our cat has got!’, and then comments, ‘I don’t suppose that that was the exact wording people used, because it is an iambic pentameter, and rhymes with “Nay, if you brave me, then you go to pot”’.
—Partridge, Dictionary of Catch Phrases, 2nd ed., 1985
However, Googlebooking the phrase suggests that the phrase has a wider use than the sartorial interpretation put forward by Ware. It is used as a gibe against anyone "putting on airs", pretending to a finer status than they're entitled to. For instance:
Kath. Sure, it’s nothin’ to do wid a lady like me.
Den. Lady like you? Oh, hullaboo, what a tail our cat’s got tonight.
—anon., Kathleen Mavourneen†
This makes a lot more sense in context. Orwell has nothing to say about de Crèvecoeur's volubility, but throughout the essay he repeatedly accuses him of intellectual phoniness and pretentiousness—putting on literary airs.
Phrasing this as "Our cat and another" is I think colloquial shorthand: Orwell mock-politely casts his use of catchphrase as a distant allusion with indirect application, and then reverses course like a whiplash, aiming straight at de Crèvecoeur. You may paraphrase:
Our cat has a fine tail, hasn't she?—and she's not the only one, Hector!
† I suspect that the phrase in fact takes its origin from the swaggering erect-tail posture of a content and self-complacent cat.