Dave, I didn't try to install both before asking my question. Thanks very much for your reply.
Yes, they are both full Ultra versions. I'm happy to report that both installed successfully, and separately. They both seem to be functioning properly. (Version 16 is a 32-bit app; version 20 is 64-bit. Thus they installed into different directories. Perhaps this helped to keep 'em separated.)
I can further report that PDVD 16 plays 3D discs in 3D mode on my new hardware, which is Intel HD Graphics 630 on an i7-7700T CPU. No separate video card. (I Googled this and got no definitive answer, so maybe Google will find this post for someone else someday.)
Thanks again Dave,
Phil