MIG wins most of the time. Like many others here I learned on stick using some pretty heavy industrial machines A3 PH lincoln and some pilot arc machines,( is that what you all call buzz box?)
I liked welding and took to it pretty quickly and easy. That was in the early to mid 60's never heard of MIG back then. but we were experimenting with TIG for welding 1 inch thick sections of Aluminium, it was a pretty impressive process.
When I finished my apprenticeship and left the trade, not that I didn't like it, just that other jobs paid much better, I realised that I enjoyed welding so bought myself a stick machine, with all the bits, and was able to make a bit on the side doing small welding jobs. It wa s a 240V single phase, 15A input with high and low volt range and choke for varying the Amps. With all copper wire transformer it was a pretty good machine. I only sold it a couple of years ago,about 3 years after buying a 3 way MIG TIG and stick machine so I had no further need for it.
It is true that that old stick machine could do a much heavier single pass weld than the MIG can, but there is nothing wrong with multi pass when and if needed. I never need to weld anything thicker than 10mm, and rarely more than 6, so MIG is good for me. I have not yet ventured into using mig for Aluminium, nor have I Tried TIG, The expense and learning curve put me off, and I'm not sure I need it. I do very little work in Aluminium or stainless If I can't stick it together with MIG or stick there is always oxy acetylene.
In fact I've even used oxy for welding Aluminium, looks pretty rough, but it works. I'm also interested in trying these new low temperature aluminium rods with a torch, I guess it's more of a brazing process, but I've heard its pretty strong, and some of the video's I've seen it looks pretty neat, but I guess that's just practice.