Honestly, you can't go badly wrong with either — both are low-VOC, water-based, climate-conscious British brands built for buying online without trekking to a merchant. But they're not identical, so let me split them properly.
COAT has the bigger range at 137 colours, with its real strength in neutrals (31) and whites (27). That matters because neutrals are where most people actually paint, and a deeper palette means more chance of nailing the exact undertone for your light. COAT's flat matt covers well, dries to a properly modern dead-flat finish, and their peel-and-stick samples are the best in the business — you stick them on different walls and read the colour in real light without a single brushstroke. Mindful is a cracking warm-leaning neutral, and Duvet Day is a lovely soft off-white that sits beautifully in north-facing rooms.
Lick is leaner at 99 colours, but it punches above its weight on greens (19) and blues (13) — so if you're after a moody green snug or a calming blue bedroom, Lick's curated palette is genuinely strong and the photography helps you visualise the scheme. Their durable matt is hard-wearing and good for family spaces.
The "but what about whites" question: both do clean, usable whites. Lick White 01 is a bright, fresh white and White 07 a softer, warmer one — straightforward and reliable. COAT's white selection is broader if you want to fine-tune the undertone.
Price-wise they're in the same ballpark, both well below the heritage brands. Coverage is where COAT just shades it in my experience — fewer surprises on the second coat.
My practical advice: order samples from both for the exact colour you're chasing, stick them up, and judge them morning and evening before committing. The brand matters less than getting the undertone right for your room's light — and on that, COAT's sample system makes the decision easier.