Which carries more authority from a coin buyer's view, a certificate of authenticity or a third party grading like PCGS?
Why the CAPS lock? COA is nice depending on what you are selling. This is kind of a loaded question. Grading by PCGS will make certain coins more liquid, but they also get authentication wrong.
I'd say a slab from any of the big 4 - PCGS, NGC, ICG or ANACS proves authenticity and gives you a very good idea of the grade, if it's not dead on (which it usually is). A COA? Maybe if it's from Sotheby's, but in general, as others have noted, you can print one on your computer. THIS MESSAGE IS AUTHENTIC - Certificate of Authenticity guaranteed...
I wouldn’t pay to slab anything under $100 in possible value If already slabbed, I’d only pay raw value Buy the coin, not the container Over $200 needs TPG, COA holds little weight for most coins
There are a couple of sellers on ebay offering empty coin cases some with COA. As stated, purchase the coin not the hype.
How many people can afford the equipment and materials to make a realistic PCGS slab? You can go into many public libraries and use their computer equipment for free.
And a TPG slab not only authenticates a coin but also indicates whether it's been damaged or tampered with. And of course there is the grade.
With the more modern stuff, some collectors want the original box and cert. Nothing wrong with that. Not important to me but some have to have it. We all collect in different ways.
TPG grading. As was said, anybody could print a certificate of authenticity on their computer in 2 minutes.
What I love is when the BEP includes a COA with an intaglio print. Really, I doubt that anyone who can successfully fake a security-printer's intaglio will have trouble with faking an offset printed COA. And as was mentioned above, you can buy COA's on eBay. The only value of a COA is what Idhair said: Some people want complete original packing.