Are their advantages of one size Thermocouple fitting over the other?

Which would be the preferred size 1/8" or 1/4 inch NPT?

Thanks

 

I'd personally choose the larger one. 1/4 NPT threads will hold better, are less prone to wear and tear and corrosive erosion than smaller ones. The 1/4 NPT takes a larger wrench so it's more robust and you can usually find replacments easily.
Excessive heat internally will not be so hard on the thermocouple since it has more mass to disapate the heat into the surrounding cast iron or steel with.
Just my choice.