A good brown heel looks like it belongs with everything in your hand luggage. A poor one looks like a shoe that was brown because the red and black had sold out. You can spot the difference from across a room, it's in the depth of the colour and whether the heel itself matches the upper or was clearly bought from a different, cheaper pile.
Brown earns its outing for most of the year in a way black doesn't quite manage, it sits happily under tailoring for an autumn wedding, under a slip dress in September when it's too warm for boots but you want more than a sandal, and it does something kinder to bare legs in summer than black ever will. What it struggles with is cool, icy colour palettes, put it next to a cold grey or a true navy and it can look like it wandered in from another outfit entirely. Tan and chocolate brown are not the same thing and treating them as interchangeable is how you end up stood in a doorway looking like your shoes had a different morning to your coat. Check the heel and sole colour matches the upper tone before you buy, in the shop, under proper light, not the warm orange glow that makes everything look like a cognac. Hold it against your bag if you're bringing one, not to match exactly but to see if they're fighting.
They age well if you let them, which is the honest selling point of brown over black. Scuffs show less, the colour tends to deepen rather than look tired, and a real leather pair will take a light polish every few wears and come back looking cared for rather than new, which suits a shoe you want to have an opinion about by its third winter. Suede brown heels are a different animal, lovely for a few months then sad looking by spring unless you're disciplined with a suede brush and keep them away from wet pavements, something I learned the hard way in a pair that spent one rainy October looking like a drowned mouse. Patent brown is its own thing again, sharper, needs wiping not brushing, and reads more evening than the matte version.
They are the wrong choice for anything deliberately monochrome, and for very formal black tie, where they'll look like an afterthought no matter how nice the leather is.
Tomorrow I'd put mine with wide leg cream trousers and a plain white shirt, nothing else competing for attention.