I think both are slippery, and would require solid batons for the horse to put his feet between to stop the foot from slipping.
Carpet is not seen so much now, it has by enlarge been replaced by rubber as it is longer lasting and does not absorb the water.
My favourite is a rubber covering that had large solid batons moulded into the rubber itself. Even the area between the solid ridges has smaller sharp ridges. Most of the newer lorries seem to be fitted with this now.
I used reject conveyor belting from the local quarry. The belts wear out quickly and are regularly replaced. Of course, it can be slippery but I fixed oak battens every 8 inches to reduce this to the minimum. The most expensive part was the oak battens as the belting was free.
Carpet fixed upside down might also work. Or coconut matting.
What about Protectakote? High tech paint, you can mix granules in it for extra non-slip - but it does need a week to cure. Speak to their tech guy, he is very good.
Perhaps add some hardwood battens.....
I have chequer plate, but that's probably not ideal.