A polished finish is glossy and brings out the colour and outlines of the stone, bringing small details to the surface and highlighting hues and colours as the light bounces off the stone.
A honed finish is more satin/matte and does not reflect light as much as the polished finish, it is smooth and flat and gives an illusion of being lighter in colour.
Examples of honed (left) and polished (right) concrete floors.
When deciding which finish you prefer, the answer depends largely on your lifestyle. If you are fond of decoration and colour, then you would choose a polished finish to show off the details. The polished finish is better for less-trafficked areas to not damage/wear down the floor, however there are still measures that can be taken to minimise this.
If you aren’t bothered by imperfections in your flooring, you will prefer honing. If the floor is in a high traffic area this is the best option. It also means you will not have to see any little scratches or etching that can be irritating to some. Spaces such as offices, swimming pools and countertops are all better suited to honing, they are also matte which will make the space less slippery when wet and therefore safer in a high traffic area.
Both honed and polished are great options and will bring your area to life, when sealed properly and cleaned regularly, they should remain in great condition no matter the finish. Ultimately it comes down to personal preference on whether you would like a matte or glossy finish, decide on how busy the room is with foot traffic, if there is a high chance of liquid spills or simply if you would like a more understated area.