Is there any fact in this example welding scenario.; long welded seam for rear quarter replacement, utilizing TIG welding over MIG welding due to the MIG weld exhibiting more show though upon finishing , due to the MIG welds hardness vs adjacent metal /shrinking /expanding ?

there will be significantly less warping with TIG welding over MIG welding.
after welding the TIG weld areas will be much easier to work with if it warps and you have to move some metal around.
MIG welds are more brittle and will crack much easier over TIG welds..

100% agree with MrT2U..............plus there will be significantly less pinholes in a TIG weld compared to a MIG weld - not even a comparison really.

No, there is no fact.

At the end of the weld, it depends on who is running the welder. Someone who doesn't know what they are doing can warp any panel with any welder.

As for pinholes in MIG welds, again, that is the person running the MIG, not the process's fault.

If anything, the MIG is faster which should produce less distortion. I just picked up a Multimatic 220, so, I can do both processes.

My Miller Syncrowave TIG 500 machine will weld up to 650 Amps, My smallest MIG welder Hobart 140 amp machine with .023" wire is all I mainly use for sheet metal . A damp rag is useful to keep things moving and under control. I assume we are not comparing flux core Mig to TIG, correct, which is not what i would use no matter what.

To clarify ; was told by someone some time ago ... that mig welding , even done expertly, will show in transverse as well as longitudinal seams due to the density /hardness of the mig weld process{.if I remember correctly} due to different expansion rates of expansion weld vs adjacent sheet metal , even ever so slight .example black car hot day in the sun will show a shimmmer ??

So park on the shade?

Seriously never heard that before, but I don't doubt the science behind the thinking, except if the end result is that critical ( and show quality black is), I would think Tig would be a worse problem for welding distortion, unless welder was willing and paid enough to go 10X? slower with the TIG , process.

If done correctly, I've never seen this happen before. I did body work for a living for a few years and have done it on the side for years since.

I did a bunch of patches on a truck that I recently saw at a car show in the heat, I did not see one spot where the patches are and I know exactly where the patches are.

Have I ever seen this happen, yes but, based on the quality of the rest of the job, I would venture to say that the patch was done incorrectly. Never have I seen this with any patch that was done by someone that I know, that also knows what they're doing.

With that said, I believe what you're describing is possible under the right circumstances, just not probable. Years ago, I did a bunch of work on SCCA race cars, which included a lot of fiberglass fender flares attached to steel bodies, etc. With those, you could see some lines in the sun where the different materials met, which was due to what you're describing. But, again, that was with steel, fiber glass and body filler.

Again, no. Whoever told you that doesn't know schitt from canned Rhubarb.

Grind the weld flush, primer, filler, skim coat, primer, and then paint covers the metal. Done properly the weld is invisible after grinding it flush.

My buddy is a mechanical engineer. He absolutely swears that on dark cars you will eventually see the mig lines if you use a mig. I have personally never experienced it.

You are 110% correct, your buddy is not. Next time you see your buddy ask him if he knows what a Metallurgist is? Ask Him what part of Physics and Math is related to fusion of metal? Ask him what the "70" means in a 7018? Pass this on to him if he thinks you are a "know-it-all":

Metallurgy

Pretty dry stuff which is why I switched from Metallurgy and welding to Environmental Sciences.

Final word on this: Most of this topic is really just poor body work and poor welding skills.

So if someone was going to buy one welder, that would be able to do most everything nicely, a TIG welder is the one to buy? For a DIY'er, who may not weld a lot and has minimal skills (using a MIG, never TIG welded before), which unit would be "good enough" for a budget and how difficult is it to learn how to TIG weld properly? Can you learn via by practicing or do you need a proper class?

Depends on your budget?, but welders are like garages, never big enough/always lacking options, so go big as your budget allows, invest in a QUALITY machine(s) new or used

As far as tig, if you can stick weld/ARC (which should be your most basic welding skill possessed) you can TIG, you just need to learn the machine and some do's and don'ts of techniques/application, everyone has a preference as to how they handle bodywork/fabrication, myself I employ ARC/MiG/Tig into my work so I need a variety of machines along with options like spool guns for aluminum....

Personally for the beginner on a small budget I'd recommend a 208/220 MiG like a Hobart/Miller 175/185 series, the smaller 120 volt machines will struggle with anything thicker than 1/8 steel...

Mike