As a follow up to my above, it's the weight of the forest that matters. Older forests typically fit bigger and denser and heavier trees, so the age of a forest still matters a lot. But a fairly established forest like the Amazon is not changing the amount of oxygen out carbon dioxide in the air unless it's expanding or contracting
There is no active sequestration for a static forest. Only if the forest is expanding in size will sequestration occur. Obviously reducing the size via burning has the opposite effect
And I'm not qualified to answer what happens when you burn down an entire millenia-old ecosystem. Seems plausible that it might not go straight back to its old self in a human-relevant timeframe.
Plants pretty consistently are ~40-50% carbon by mass, so the amount of biomass on the ground is a fairly solid indicator of the amount of carbon sequestered. Unless the ranchers have a truly massive amount of hay at all times I don't see how a ranch can approach a forest.
Don’t forget the soil. Old prairie has immensely thick soil, with a high carbon content. Think deep plant roots. With the right management, ranchers could mimic the prairie ecosystem, restore and build soil, and sequester carbon into the soil. It’s not easy, but the most successful farmers have been astoundingly successful.
Not that any of this is a valid excuse for burning down the Amazon.
It may be a click-bait factoid, but it's not like that factoid isn't an important one.