Here's my opinion. I'm not a licensed plumber, but I do a fair share with bathroom remodels and other light plumbing installation and repair, and I have a background in several sciences.
Clearly the putty is a different category, and you've figured that out by now.
The issue is dope vs. tape, and frankly most of the answers even by pro plumbers make no logical sense. If you think about what's happening with the materials, using them together is pointless.
Let's say you're one of those that uses both tape and dope. So first you put your tape on, then the dope. Well, what happens when you screw that joint together is that one side of the threads has only tape touching it (the tape basically keeps the dope from touching that side), and the other side has dope touching it. They can't both be best.
Both are lubricants. Both help seal the micro gaps in the joint to resist water leaks. But they can't both be best at that job - only one or the other are. Use only the one that is best. That one will touch both sides of the threaded joint.
Personally, I think the best lubricant and the best long term sealant is pipe dope. I use this on shower arms, threaded nipples, and female PEX adapters on threaded shower valves. On any connection where there is a compression or gasket seal, it only gets in the way and gunks things up (except maybe as mentioned by Jeff Young above - then a small amount is acting strictly as a lubricant). If those leak, there is a different problem, such as a little piece of debris, crack, misalignment or other issue that needs to be corrected first.