(1) Background: Malnutrition frequently affects patients with cancer, and it negatively impacts treatment tolerance, clinical outcomes and survival. Thus, appropriate nutritional screening and early nutrition support are extremely recommended. Currently, a significant number of oral supplements (OS) are commercially available; despite this, there is a lack of evidence for recommending specific OS, including leucine-enriched OS, for nutritional support in patients with cancer. (2) Aim: To compare the clinical evolution of patients with cancer (undergoing systemic treatment) that received standard hypercaloric, whey protein-based hyperproteic oral supplements vs. hypercaloric, hyperproteic leucine-enriched OS using a novel morphofunctional nutritional evaluation. (3) Patients and methods: This paper details an open-label, controlled clinical study in which patients were randomly assigned to receive nutritional treatment with whey protein-based hyperproteic oral supplements (control group) vs. hypercaloric, hyperproteic leucine-enriched OS (intervention group) during a twelve-week period. Forty-six patients were included; epidemiological, clinical, anthropometric, ultrasound (muscle echography of the rectus femoris muscle of the quadriceps and abdominal adipose tissue) and biochemical evaluation were performed. All patients received additional supplementation with vitamin D. (4) Results: Nutritional parameters (including bioimpedance, anthropometric, ultrasound and biochemical variables) of all included patients remained stable after the nutritional intervention. Extracellular mass tended to increase in the patients that received the leucine-enriched formula. Functionality (evaluated through the stand-up test) improved in both groups (p< 0.001). Prealbumin, transferrin levels and superficial adipose tissue increased in the control group (p< 0.05), while self-reported quality of life improved in all the evaluated patients (p< 0.001). (5) Conclusions: Nutritional support with hypercaloric, hyperproteic (with whey protein) OS and vitamin D supplementation were associated with the maintenance of body composition and improvements in functionality and in quality of life in the patients with cancer undergoing systemic treatment. No significant benefits were observed when a leucine-enriched formula was used.