Nereus said:"Is the LuxIII better at taking the higher current/heat than the LuxI..."
Basically the answer is yes, but the difference is not very big. According to datasheets the junction-to-case thermal resistance is 15C/W for Lux1 and 13C/W for Lux3. If, for example, you run both lux1 and lux3 at 3 watts and keep the slug temps at e.g. 40C, the Lux1 junction is running at 85C and the Lux3 junction is running at 79C.
Hope this helps.
-N