Tig welds are way stronger, but you need a tig machine and there not cheap. Im not a professional but i tig and mig weld from time to time. Tig takes some time to get the form down smooth. Its a lot more intricate but the way the metal puddles and beads makes it overlap and bond better than just a mig weld.
Also the wire in your mig welder is harder than the rod used in tig welding, and ive found that in high stress areas of force or high heat areas the harder mig wire seems to crack easier. Thats basically a basic overview but i hope it made some sense.
You can still mig weld your exhaust and it should be fine as long as its not headers