Is it okay to simply remove the SD card from an RPi B+ and put into a RPi 3 B and have OctoPi/OctoPrint boot and function normally or do I need to build a fresh SD card?
I see no reason why that wouldn't work perfectly. And yet, I still would re-image with a brand new OctoPi installation.
There are subtle hardware differences in the underlying computer-on-a-chip that's at the heart of all this.
I went ahead and tried it and it worked flawlessly. It probably helped that I had just upgraded the image for the RPi B a few days prior but just popping the new RPi 3 into the case with the old RPi's SD card worked fine. Thanks.
For what it's worth, there's a beefier Broadcom main chip on the new one. It's possible that starting from scratch would bring in a different driver for that but you never know.