Yes, I agree, it is slower and you need pure argon ( for MIG you can use cheaper CO2). Some sources claim a thermal distortion is lower in case of TIG welding so I assume the heat you put into material is lower as well. The thickest part I TIG welded was 8mm steel plate with 16 mm bar, but it was at the very beginning of my TIG welding adventure with little experience in welding (see pic below) and I'm by no mean I was professional welder.
Click image for larger version. 

Name:	tig.jpg 
Views:	11249 
Size:	44.3 KB 
ID:	3948
Of course it is possible to weld with sticks If there is an option in TIG inverter. In summary TIG initial an running cost is higher, but there is no spatters, post weld clean-up and is more precise. You just need to decide what needs do you have and choose suitable welding technique.