Planets in binary systems are a fascinating and yet poorly understood phenomenon. Since there are only a few known large-separation systems in which both components host planets, characterizing them is a key target for planetary science. In this paper, we aim to carry out an exhaustive analysis of the interesting XO-2 system, where one component (XO-2N) appears to be a system with only one planet, while the other (XO-2S) has at least three planets. Over the last 9 years, we have collected 39 spectra of XO-2N and 106 spectra of XO-2S with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems (GAPS) project, from which we derived precise radial velocity (RV) and activity indicator measurements. Additional spectroscopic data from the High Resolution Echelle Spectrometer (HIRES) and from the High Dispersion Spectrograph (HDS), and the older HARPS-N data presented in previous papers, have also been used to increase the total time span. We also used photometric data from TESS to search for potential transits that have not been detected yet. For our analysis, we mainly used PyORBIT, an advanced Python tool for the Bayesian analysis of RVs, activity indicators, and light curves. We found evidence for an additional long-period planet around XO-2S and characterized the activity cycle likely responsible for the long-term RV trend noticed for XO-2N. The new candidate is an example of a Jovian analog with msini~3.7M_J_, a~5.5au, and e=0.09. We also analyzed the stability and detection limits to get some hints about the possible presence of additional planets. Our results show that the planetary system of XO-2S is at least one order of magnitude more massive than that of XO-2N. The implications of these findings for the interpretation of the previously known abundance difference between components are also discussed.