These two aren't really direct rivals, mate — they sit at different price points, so the honest answer depends on what you're after.
Crown is your dependable mid-market workhorse. It carries 193 colours, with genuinely strong neutrals (33), greys (32), whites (27) and blues (22), and an LRV range running from 4.1 right up to 100. The coverage is good, it goes on nicely, and it's widely stocked. If you want a clean, no-drama white for ceilings and trim, Crown Pure Brilliant White and Crown Bright White do exactly what they say — crisp, neutral, reliable. For most family homes on a sensible budget, Crown gets the job done with no complaints.
Dulux Heritage is the step up. It's a smaller, more curated range — 112 colours — but the colours have more depth and pigment character, the kind of complexity you normally pay Farrow & Ball money for. Strongest families are neutrals (27), whites (26), blues (13) and greens (13), with LRVs from 3.7 to 86. Their off-whites are where it shines: Dulux Heritage Indian White and Dulux Heritage Panel White both have a softness and warmth that flat builder's white can't touch. The eggshell and the matt have a lovely chalky-but-tough finish too.
The "but what about cost?" question is the real decider. Heritage is noticeably dearer per tin. If you're painting a whole house and watching the budget, Crown stretches further. If you're doing a feature room — a hallway, a snug, a dining room where the colour earns its keep — spend on Heritage and you'll see the difference on the wall.
Practical steps: order sample pots of both, paint A4 patches, and live with them a couple of days through changing light. Nine times out of ten the Heritage colour reads richer and the Crown reads flatter — and that tells you instantly which one your room wants. Don't choose on the tin; choose on the wall.