Hi Peter,
GP wouldn’t have any settings in the customizer that would alter how the plugin displays those contents, especially you are also using beaver builder.
I can see Next and Prev links on both sites – they are just in different style so I assume there would be those settings in the plugin?
“16 matches” would also show up on this site: http://bob-cheryl.ptest2.com/our-listings/ if you click the arrow to go to next page.
The contents of individual property pages are entirely displayed by the plugin as well so I’d say check if you have all the settings the same for both sites?
If you’ve already done that then I would recommend asking Rover IDX for help.
Hope this helps!