Honestly, you can't go wrong with either — both are top-tier and you're paying for properly pigmented, beautifully nuanced colour. But they pull in different directions, so let me sort it for you.
Farrow & Ball has 301 colours and is the one everyone knows. Its strength is depth — that slightly chalky, light-shifting quality you get from heavy pigment loads. The palette leans hard into greens (67 of them) and blues (41), with a brilliant neutrals range too. LRVs run from 5 right up to 92, so you've got proper inky darks through to near-whites. Something like All White is their cleanest light, while Acid Drop shows the other side of the range — F&B will happily do a punchy, saturated statement colour as well as a muted heritage tone.
Paint & Paper Library has a tighter 186-colour palette but a smarter trick: their colours are organised into tonal "stacks" — the Roman numeral suffix tells you how dark a shade sits within its family. Slate IV and Lead II are perfect examples; you can build a whole scheme using lighter and darker versions of the same hue across walls, woodwork and ceiling. It's a genuinely useful system for getting a cohesive, layered room without guesswork. Their strengths are greens (34), neutrals and a cracking whites range (31), and their LRV span is even wider — 3.7 to 99.2.
The "but what about durability?" question: both wash and wear similarly well in equivalent finishes, so that's not the deciding factor.
My steer — if you want that recognisable, atmospheric F&B look and the broadest choice, go Farrow & Ball. If you're decorating a whole space and want a clean, modern, tonally-coordinated scheme with minimal fuss, Paint & Paper Library's stacking system is the cleverer tool. Order samples from both and live with them on the wall for a couple of days before you commit — that's the only test that actually matters.