How much does square tubing deform under heat? Is it better to stick or mig weld?

Yes just to get us going.
Welding methods.. whats it all about.
MIG is Metal Inert Gas, sort of arc welding with a gas* flux and wire feed allways.
TIG is Tungsten Inert Gas as above ish there is ac dc hand fed filler sometimes gas only very flexible.
Stick or arc is cheap the consumerbles are the flux coted electrode that becomes the filler.
Gas Fuel for brazing joining with or without filler no power required unless spark ignitions required.
any thoughts?.

How much does square tubing deform under heat? Is it better to stick or mig weld?

Not 100% sure, but I'm willing to bet the heat input is just about the same.

ARC vs. MIG? ARC every time hands down for structural work.

Why?

During the ARC welding process, you take advantage of the flux and chemical compositions in the ARC welding rod, which can change the properties of the weld it's self which seems to be far beyond what can be done with bare filler material or rod.

The other major advantage is you can just about garantee an ARC weld just by looking at it. Bead shape and form, if there is a major problem, the slag will tell the story. Incomplete penetration usually leaves slag stuck in the edge of the weld, to where as MIG can just simply lay on top and look pretty.

MIG welding is great for production work because you don't have to stop to change rods and it requires less skill which means it's easier to train someone to do production MIG welding, and although I'd hate to say it, you can pay them less. My problem with MIG welding is that you can't always judge a weld by looking at it. I've personally seen MIG welds that look great, and just rip right back out....

MC

Not sure what the question really is. Square tubing comes is a bunch of different sizes andf I'd agree with MC that a well chosen rod in the right buzz box will do a good job but maybe if the metal of the square tubing is thin , like with furniture, you will have to mig it. Mig is ok and it is great at filling gaps but if the parts are cut well, thick enough and clean then a stick welder would be a good way to go.
To answer the question I do not know that I have seen square tubing distort under heat. Depends on a lot of things but the main problem I look out for is the distortion of the weld as it cools...obviously get the work tacked up and in position before you weld. It might still distort a bit after it has been welded but you'll be fairly near what you had wanted.

As in all welded entities, a tube-to-tube welded joint will have longitudinal reduction of the final tension member. In the case of square tubing, a tube-to-tube butt joint will have a dimensional reduction of the face of the tube being attached to. In simple terms, the tube will bow towards the tube welded to it. This can be severe in all but the heaviest section tubing. Restraining the welded-to tube can help a lot but results in higher residual stresses within the weld. This can lead to cracking, now or later. Preheat(I know, we all hate it) and lowered heat input both help. In reality, most square tubing joints are done with little or no prep other than cutting to length. This gives you two different joint configs, each with their own issues. The two faces that are nearest to perpendicular are restrained, tight-fit butts that suffer from poor fusion. The side or parallel faces, due to the rounded corners of the tube, have an excessive gap and an exposed edge to contend with giving you the potential for burn-through and exposing the " running" tube to the most deforming force of the whole assembly. Probably more than you wanted but less than you need.