(1) Background: Alcohol consumption is one of the main causes of acute pancreatitis. (2) Material and Methods: In this unicentric retrospective cohort study, we selected 1855 patients from the Bucharest Acute Pancreatitis Index (BUC-API) who presented with acute pancreatitis. We investigated correlations between Alcoholic Acute Pancreatitis (AAP) and the rate of complications, cost, length of hospitalization and rate of recurrence. (3) Results: We found a moderately strong association between AAP and recurrence (p < 0.01) and observed that the disease is likelier to evolve with pseudocysts and walled-off necrosis than other forms of AP. Patients with AAP are less likely to have a morphologically normal pancreas than patients suffering from AP of other causes (p < 0.01), but a low probability of requiring intensive care unit admission (p < 0.01) significantly lowers daily cost (Md = 154.7 EUR compared to Md = 204.4 EUR) (p < 0.01). (4) Conclusions: This study’s data show that patients with AAP have a greater rate of pseudocyst occurrence, lower intensive care unit admittance rate and lower cost of hospitalization than patients with AP of other causes. Typical Sketch: A middle-aged male tobacco smoker with recurrent AP, lower risk of in-hospital mortality and complications such as pseudocysts; treated in a gastroenterological ward and discharged at-will.