In laser cutting one is more interested in knowing heat flow in solid in order to determine the metallurgical changes in sheet (or part) being cut and also to know other mechanical effects like distortion. For this FEM is definitely more suitable. Magnitude of error will depend upon the accuracy of data and assumptions made during modelling, which is true of any numerical method.

Thank you sir, I'll try using fem.

You may also have a look at my short note entitled 'Note on FE analysis of heat flow using point, line, surface, volumetric moving heat source' at my researchgate webpage. Best wishes,