When would you use a puncture resistant tire vs. a puncture resistant tube?
My choice would be based on my current need. How often are you getting punctures? How efficiently can you make repairs? Are you commuting to work where the delay from a flat repair results in lost wages or potential job loss? Then go with puncture resistant tires. Then add the flat resistant tubes if needed. If your tires are fairly new but prone to punctures, I would go with new puncture resistant tubes based solely on the cost. If I needed new tires and was primarily concerned about punctures I would get puncture resistant tires then add tubes if needed.
From my experience in mountain biking the tire is much more important than the tube. I have not heard of puncture resistant tubes with a special layer. I assume these are just heavier and thicker tubes. Many friend and I ride/rode 185g tubes from a major brand here in Europe on 2.5"x26.0 tires. Some tried even lighter ones. Years ago we tried heavier ones (up to 450 g). But those did not work better than the much lighter ones.
When riding offroad the most common punctures come from a hit on a rock where the tube gets pinched between the tire and the rim flange (pinch flat). If it happens on both sides it's also called snake bite. What helps against these types of punctures are tires with stronger side wall casings (carcasse) or more air pressure.
If you have mainly punctures because of stitches you should try a tire with a special layer which prevents these.
But the more puncture resistant a tire is the heavier it is and also the rolling resistance increases.
On my enduro mountain bikes I'm riding tubeless tires for 10 years now. On my old bike I had about 4 punctures in 5 years. On my new bike last year I had zero punctures. I ride a lot and sometimes even races. On my old downhill bike I still ride the 185g tubes because the rims have some dents and I do not have punctures very often. Since last year I also ride tubeless on my commuter bike with 1.5" gravel tires.
Tubeless tire setup is the most puncture-resistance you can ask for. When your tire gets pricked by a thorn, sliced slightly on a rock or pinched against the rim, air will leak out of the tire, but sealant will also leak out of the same spot. Sealant is designed to clog this hole and "glue" it shut.
Like noox and mikes have said, tubes aren't the solution. It's in the tires and how you set them up. It also depends on your intended use. If you're riding road or mountain bike on expensive bikes, definitely go tubeless. If you're just doing urban commuting, maybe consider a full rubber tire, but you'll be compromising comfort and speed and adding weight.