I'm a big fan of both and my decorators are/ have been happy with both too.
F&B do "curation" of their palette extremely well; as there is only ever a limited number of colours to choose from, it's easy to "learn" their colour card and match their colours. The colours are beautiful and work really well in dingy British light. I rate their emulsion highly and have used extensively in my house.
I also love Little Greene, their range is bigger but still manageable (having 3 million colours to choose from is pointless), colours can be more vibrant but also really like their colour "families" in the neutrals eg Slaked Lime, French Grey etc. So we have used French Grey on our living room walls with the Light version on ceiling. You can take that further with the Dark shade on woodwork if you want to, etc.
Major caveat with F&B is the eggshell: it's water-based so IME chips easily. We have Railings on skirtings and stairs here and it badly needs touching up. LG have an (eco-friendly) oil-based eggshell that we've used on our front door and has worn amazingly well in the same time period as the F&B eggshell (4 years).
I also like LG's curated colour cards, the latest is "Stone" which is mainly neutrals (the hardest to get right IME). Makes it easy to pick colours that go together, much as F&B does in fact.
I would choose LG over F&B for woodwork in high traffic areas but both ranges are excellent. Go with the colours you prefer.
Caveat: every time one of these threads pops up, there will be a load of people telling you to get a colour match with Johnston's/ Valspar etc. You can of course, I've done it in the past myself, but you won't get an identical colour (whatever people tell you) and if you like the colour ranges produced by these paint businesses, then support them by buying from the people who actually came up with them.