These two aren't really fighting over the same ground, mate, so the choice is easier than it looks.
Farrow & Ball is the heavyweight. 301 colours, with a properly deep bench in greens (67), blues (41) and neutrals (38), and an LRV range running from a near-black 5 right up to 92. That breadth matters: when you want a green with genuine complexity — something that shifts through the day — F&B has more contenders than anyone. The colours have depth and pigment richness that's hard to fault, and the chalky Estate Emulsion finish is iconic for a reason. The trade-off is price and that flat finish marks easily, so for kitchens and hallways you'll want their Modern Emulsion instead.
Lick is the modern challenger — 99 colours, tightly edited, strongest in greens (19), neutrals (13) and blues (13), with whites a real focus (12 of them). It's designed for people who find a fan deck overwhelming. The peel-and-stick samples are excellent, the app-led approach is genuinely useful, and it's noticeably cheaper. The finish is durable and washable, which suits family homes. What you lose is range and that last 10% of pigment subtlety F&B trades on.
Look at the whites as a tell. F&B's All White is a pure, uncomplicated white with no underlying tint — clean and bright. Lick's White 01 and White 07 sit in similar territory but the range stops there; F&B gives you dozens of off-whites to fine-tune warmth against your light. On bolder colour, F&B's Acid Drop is the kind of zingy, confident yellow-green that shows what 301 colours buys you — Lick simply doesn't go that loud.
My honest steer: if colour is the whole point of the project — a drawing room, a statement hallway, a dark moody snug — go Farrow & Ball. If you want a calm, contemporary scheme done quickly and affordably without agonising over 50 near-identical greys, Lick will sort you nicely. Sample either properly before you commit; both brands make it easy.