Hi Peter,
The 64-bit engines will be stronger but otherwise not much difference. I would probably stay with the 32-bit versions if your DGTPi is the stock version with a Pi3b inside.
As for the web server make sure you use http://<ip address> and not https://. If you can use ssh to log into the DGTPi you can look at the log files in /opt/picochess/logs. They might show something wrong. Also, 'systemctl status picochess' is useful to look at. This all assumes the PicoChess is working for you (you can play a game and use the buttons).
Randy