So upholstery is my business (well, upholstery supply, that is, as I don't do the work, just sell the materials). I rarely get going on the topic, because well, aviation is my hobby, and once I start talking business, inevitably someone thinks you're a shill and trolling the forums for business.
Anyway, here's the skinny:
Airtex maintains patterns and makes original-like covers for airplanes. They are a niche business that is similar to Katzkin, PUI, or Distinctive Industries in the automotive aftermarket (for those of you in the classic, hot rod, or collector car world).
In years past, you would take your car, plane, or boat to an upholstery or trim shop to have the interior redone. That upholsterer would remove the seats, the seat covers, inspect/replace/rehab the foam cushion, then trace and pattern out the seat cover, cut and sew a replacement cover, and replace the seat cover over the foam. Voila, you have a newly-upholstered seat. The tracing/cutting/sewing can be very labor intensive.
Usher in Airtex. They have the patterns, and have already traced/cut/sewn the seat covers. Now, you've just cut that part of the labor out of the upholsterer's equation. Airtex manufacturers these seat covers using economies of scale (bulk buys on material, established patterns, lower-skilled cutters/sewers, etc). and then can pass them along much less expensively than it would cost for an upholsterer to do the same amount of work. Now, you can have an upholsterer (or DIY) remove the old cover, pop a new one on, and you're practically done.
Why is one better than the other? I know the materials that Airtex uses, and the materials that upholsterers and trimmers have access to, and there is a quality difference. You'll also find a workmanship difference. Why? The difference is a custom tailor vs. the mass-produced product. Airtex interiors look great. An upholsterer owns the interior and will make it look great. Their name is on it. You get much more choice in the matter when working with an upholsterer. They can do designs. They have access to many more colors. They can embroider. They are your personal artist. The difference is like using a custom paint job vs. a stock one. Airtex is higher price for the materials/lower price for the labor, and an upholsterer is higher price for the labor/lower price for the materials.
Don't be discouraged if you get a high quote from an upholstery shop. Typically an upholstery shop will be on par with a completed Airtex interior (unless you do it yourself, of course). Certainly upholsterers are like any other mechanic... their price depends on how busy they are, how much they want the job, etc. You should get 2 or 3 different quotes and you'll see wild differences.
When my interior goes to get done, I plan to have a good auto upholsterer do the job. I have the luxury of knowing who the good shops are, and if you'd like to PM me, I can let you know some good shops in your area, as well. My company covers the Midwest pretty decently, so if you're outside of the Midwest and Southeast, I may not have a good lead for you. But, can't hurt. You'll pay extra cash if you have an aircraft interior company do the job... because well, if it's aviation, add a few zeroes and commas... and the only thing they have is a shop on the field.
Again, my company does not do the work ourselves, we supply trim and upholstery shops throughout the Midwest (and elsewhere). I'm happy to help out, if you have any interior questions.
The burn cert is FAR 25.853. It runs around $75 (IIRC) to get a signed cert for each material used. We do this frequently for customers.