I couldn't find a fair comparison. Let's the compare the following two:
A direct air capture plant which is surrounded by solar panel farm which provides the energy to run it. It obviously runs only during the day. In a typical implementation a DAC plant captures CO2 into an alkali solution eg. KOH or NaOH as carbonate ions. Which then reacted by Ca(OH)2 to precipitate the insoluble CaCO3 (limestone) and restore the KOH/NaOH solution. The limestone is then subjected to high heat to release CO2 and store it in a tank which then can be trucked/piped away. The reactants are recycled. So power is needed to run the fans for air filtration and power is needed to bake out the limestone. (There may be less energy intensive processes I don't know about.)
A forest planted into the same area: it captures CO2 as it lives. Let's assume we collect all carbon containing parts: eg. the fallen leaves and other shedding and process them. One way to process it is using hydrothermal liquefaction which turns the organic matter into crude-oil like substance which provides a way to remove the carbon from it. What remains is a nutrient rich sludge that can be returned to the forest.
There are a lot of comparisons on the web but they often compare the net DAC plant area without the area needed for the energy source with the carbon sequestered in the wood of the forest only without considering the fallen leaves and stuff.
My question is which of the two can collect more CO2 per area per year? Are forests better at capturing CO2 than artificial solutions.