The aim of this research work was to conduct a comparative study on the effectiveness of the application of chemical cleaning versus laser cleaning in the removal of surface congruent dissolution products from a potash-lime–silica historical stained-glass sample. EDTA was selected as the chemical cleaning agent. Laser cleaning was performed using a 238 fs pulse UV (343 nm) laser. The comparative cleaning studies were carried out on a stained-glass piece supplied by the Maison Lorin Glass Restoration Workshop from Chartres, France. Given the complex nature, irregular thickness and heterogeneity of the encrustations found on the glass, the two cleaning approaches were carefully performed step by step, while monitoring the process using an optical microscope. Raman spectroscopy and field emission scanning electron microscopy were used to characterize the changes induced on the sample surface during the cleaning process. The results demonstrate that the two cleaning approaches were able to eliminate the outer surface dark layer associated with carbon compounds, as well as the external part of the white layer generated by the crystallization of salts, formed with the dissolved elements after a reaction with the air. A comparison of the advantages and disadvantages of each method is also presented.