Direct air capture can be based on an adsorption system, and the used sorbent (chemisorbents or physisorbents) influences process. In this work, two amine-functionalized sorbents, as chemisorbents, and three different metal organic frameworks, as physisorbents, are considered and compared in terms of some key performance indicators. This was carried out by developing a mathematical model describing the adsorption and desorption stages. An independent analysis was carried out in order to verify data reported in the literature. Results show that the equilibrium loading is a critical parameter for adsorption capacity, energy consumption, and cost. The considered metal organic frameworks are characterized by a lower equilibrium loading (10−4 mol/kg) compared to chemisorbents (10−1 mol/kg). For this reason, physisorbents have higher overall energy consumptions and costs, while capturing a lower amount of carbon dioxide. A reasonable agreement is found on the basis of the operating conditions of the Climeworks company, modelling the use of the same amine cellulose-based sorbent. The same order of magnitude is found for total costs (751 USD/tonneCO2 for our analysis, compared to the value of 600 USD/tonneCO2 proposed by this company)