In this work, two series of specimens with Hammar and Svensson's Cr- and Ni-equivalents (Creq+Nieq) = 35 and 45 wt% were used to cover a wide range of austenitic grades. These were laser welded with different energy inputs achieving cooling rates in the range of 103 °C/s to 104 °C/s. As high cooling rates and rapid solidification conditions could favour fully austenitic solidification and therefore raise susceptibility to solidification cracking, the solidification modes of the laser welded specimens were compared to the ones experienced by the same alloys under arc welding conditions. It was found that high cooling rates experienced in laser welding promoted fully austenitic solidification for a wider range of compositions, for example specimens with (Creq+Nieq) = 35% under arc welding cooling conditions at 10 °C/s showed fully austenitic solidification up to Creq/Nieq = 1.30, whilst the same specimens laser cooled at 103 °C/s showed fully austenitic solidification up to Creq/Nieq = 1.50 and those cooled at 104 °C/s showed it up to Creq/Nieq = 1.68. Therefore, high cooling rates extended the solidification cracking risk to a wider range of Creq/Nieq values. This work also compares the cooling rates experimentally determined by thermocouples to the computed cooling rates calculated by a highly-advanced computational model. The distance between the thermocouple's wires and the thermal resistance of thermocouples together with the small size of the weld pools proved to be practical limitations in the experimental determination of cooling rates. However, an excellent agreement was found between computed and experimental solidus isotherms at high energy input settings. For low energy input settings cooling rate was in the order of magnitude of 104 °C/s, whilst for high energy input settings cooling rate was found to be in the order of magnitude of 103 °C/s.