The high burden of influenza in children has driven numerous countries towards universal vaccination of healthy children from 6 to 59 months of age. The Region of Murcia was one of the pioneer Spanish regions to conduct a universal vaccination campaign and to use live-attenuated intranasal vaccine (LAIV) if age appropriate. This study aims to evaluate the parents’ likeliness to vaccinate their children and to compare the profile of vaccinating/non-vaccinating parents. This study was designed as a prospective, real-world, survey-based data collection in the 2022–2023 season campaign. This study’s sample was selected from those children whose information was available in the local Public Health System databases PERSAN and VACUSAN. Children received LAIV or intramuscular vaccine (IIV) depending on their age as per standard practice. The parent self-vaccination/intention to vaccinate themselves in this campaign (OR = 4.75), the compliance with the official vaccination schedule (OR = 3.41), and the prescription of antibiotics more than twice in the previous year (OR = 2.24) were strongly associated with children’s vaccination. Overall, vaccinating parents were very satisfied with the vaccine (IIV: 67.5% vs. LAIV: 68.8%, p = 0.320), and most parents would rather have their children vaccinated with LAIV for the next campaign (43.0%). The main reasons for vaccinating were to protect the child (LAIV: 85.9% vs. IIV: 89.4%), and the predominant reasons for not vaccinating were a lack of healthcare professional recommendation (30.9%), and lack of information about the vaccination campaign (21.5%) and the vaccine itself (21.0%). The clinical context of parents and children was determinant in decision making, which was also influenced by the presence or absence of recommendation by healthcare professionals. Parents were generally very satisfied with the vaccine and showed their preference towards LAIV for future campaigns.