Navigating the web represents a complex cognitive activity that requires effective integration of different stimuli and the correct functioning of numerous cognitive abilities (including attention, perception, and working memory). Despite the potential relevance of the topic, numerous limitations are present throughout the literature about the cognitive load during online activities. The main aim of this study is to investigate cognitive load during comprehension and information-seeking tasks. In particular, we here focus on the comparison of the cognitive load required while performing those tasks using mobile or PC-based devices. This topic has become even more crucial due to the massive adoption of smart working and distance learning during the COVID-19 pandemic. A great effort is nowadays devoted to the detection and quantification of stressful states induced by working and learning activities. Continuous stress and excessive cognitive load are two of the main causes of mental and physical illnesses such as depression or anxiety. Cognitive load was measured through electroencephalography (EEG), acquired via a low-cost wireless EEG headset. Two different tasks were considered: reading comprehension (CO) of online text and online information-seeking (IS). Moreover, two experimental conditions were compared, administering the two tasks using mobile (MB) and desktop (PC) devices. Eleven participants were involved in each experimental condition, MB and PC, performing both the tasks on the same device, for a total of twenty-two people, recruited from students, researchers, and employees of the university. The following two research questions were investigated: Q1: Is there a difference in the cognitive load while performing the comprehension and the information-seeking tasks? Q2: Does the adopted device influence the cognitive load? The results obtained show that the baseline (BL) requires the lower cognitive load in both the conditions, while in IS task, the requirement reaches its highest value, especially using a mobile phone. In general, the power of all the brain wave bands increased in all conditions (MB and PC) during the two tasks (CO and IS), except for alpha, which is usually high in a state of relaxation and low cognitive load. People include website navigation into their daily routines, and for this, it is important to create an interaction that is as easy and barrier-free as possible. An effective design allows a user to focus on interesting information: many website architectures, instead, are an obstacle to be overcome; they impose a high cognitive load and poor user experience. All these aspects draw cognitive resources away from the user's primary task of finding and comprehending the site's information. Having information about how the cognitive load varies based on the device adopted and the considered task can provide useful indicators in this direction. This work suggests that using an EEG low-cost wearable device could be useful to quantify the cognitive load induced, allowing the development of new experiments to analyse these dependencies deeper, and to provide suggestions for better interaction with the web.