In this article, I will discuss possible differences between ecosystems and organisms on the basis of their intrinsic complexity. As the concept of complexity still remains highly debated, I propose here a practical and original way to measure the complexity of an ecosystem or an organism. For this purpose, I suggest using the concept of logical depth (LD) in a specific manner, in order to take into account the difficulty as well as the time needed to generate the studied object. I illustrate this method with fully controlled Daisyworld simulations (i.e., simulations based on the Gaia hypothesis) that have often been proposed to mimic living systems. The method consists of the following sequential stages: (1) identification of the shortest program able to numerically model the studied system (also called the Kolmogorov–Solomonoff complexity); (2) running the program, once if there are no stochastic components in the system, several times if stochastic components are there; and (3) computing the time needed to generate the system with LD complexity. This measure is supposed to estimate the system complexity. It appears in this study that LD estimations fit well with the intuition we have of complex systems, with higher complexities being found for more realistic Daisyworlds. With such a method of capturing the time needed to build a system, we expect to detect in future studies any quantified differences between complex ecosystems and organisms.