(1) Background: Psychological factors can strongly affect the athletes’ performance. Therefore, currently the role of the sports psychologist is particularly relevant, being in charge of training the athlete’s psychological factors. This study aims at analysing the connections between motivational climate in sport, anxiety and emotional intelligence depending on the type of sport practised (individual/team) by means of a multigroup structural equations analysis. (2) 372 semi-professional Spanish athletes took part in this investigation, analysing motivational climate (PMCSQ-2), emotional intelligence (SSRI) and levels of anxiety (STAI). A model of multigroup structural equations was carried out which fitted accordingly (χ2 = 586.77; df = 6.37; p < 0.001; Comparative Fit Index (CFI) = 0.951; Normed Fit Index (NFI) = 0.938; Incremental Fit Index (IFI) = 0.947; Root Mean Square Error of Approximation (RMSEA) = 0.069). (3) Results: A negative and direct connection has been found between ego oriented climate and task oriented climate, which is stronger and more differentiated in team sports. The most influential indicator in ego oriented climate is intra-group rivalry, exerting greater influence in individual sports. For task-oriented climate the strongest indicator is having an important role in individual sports, while in team sports it is cooperative learning. Emotional intelligence dimensions correlate more strongly in team sports than in individual sports. In addition, there was a negative and indirect relation between task oriented climate and trait-anxiety in both categories of sports. (4) Conclusions: This study shows how the task-oriented motivational climate or certain levels of emotional intelligence can act preventively in the face of anxiety states in athletes. Therefore, the development of these psychological factors could prevent anxiety states and improve performance in athletes.