These two get pitched against each other constantly, and honestly they're aiming at different things.
Farrow & Ball is the heritage name. 301 colours, with genuinely deep ranges in greens (67), blues (41) and neutrals (38), and an LRV range running from a near-black 5 right up to 92. The pull is the colour itself — those layered, complex pigments that shift through the day — and the chalky Estate Emulsion finish. The downsides are well known: it's pricey, the matt finishes mark and aren't always easy to wipe, and you'll often need more coats. A colour like Acid Drop is exactly the sort of punchy, characterful shade F&B does that few others match.
COAT is the modern challenger. Smaller library — 137 colours — but well-edited, strongest in neutrals (31), whites (27) and greens (24), with an LRV range of 4.1 to a very bright 99.3. The paint is water-based, low-VOC, genuinely washable, and goes on with cracking coverage and a dead-flat finish. It's also cheaper, sold direct, and the tester-to-delivery experience is slicker. Mindful and Duvet Day are the kind of calm, liveable shades COAT does brilliantly.
The usual "but what about" — *does COAT look as good on the wall?* On flat, even light it holds its own; what F&B gives you is more pigment depth and that subtle movement in changing light, which matters most on big feature walls and in period rooms. For a hallway, kids' room or rental, you won't miss it — and COAT's durability is a real advantage.
Whitewise, All White is F&B's clean, uncomplicated white; COAT's whites lean similarly fresh but wipe better.
My steer: COAT for high-traffic, practical spaces and anyone wanting tough paint at sane money; Farrow & Ball when the colour itself is the whole point — a deep green dining room, a period drawing room, a moody bedroom. Order testers from both, paint them side by side on a board, and view them morning and night before you commit a penny.