I have the ChannelLock 410 pliers that I bought when I was a auto mechanic, about 53 years ago. They look like your old pliers and like yours, are as smooth as silk. I still use them to this day, as a matter of fact just used it yesterday to get a bolt out that was froze in place. In my opinion, these are the best pliers in the world.
I absolutely love my 337's. They belonged to my grandfather and are probably 30 years old. I use them all the time and they can still cut string. They make a great tool, my grandfathers No420 champion Dearment channellocks from 1933 are still going strong as well. The teeth have some wear but they still grip enough for me. Btw I'm pretty sure those cutters you just bought can be had for a but less, more like in the $12 range.