What is the difference between these two battery setups in parallel?
You haven't put dimensions into your big sketches, whose relative lengths seem to be contradicted your little sketches, so it's not possible to tell.

If the big diagram is wider than it's tall, so if the new battery is a long way from the original pair, then setup 1 uses physically the least length of cable, and will have lowest overall resistance. However, the new battery will share less of the load, especially a high current load, due to the voltage drop on the cables. This will still be 'better' than without the third battery.

A setup you've not shown is to connect the third battery directly to the feed terminals. This may use less total cable than setup 2, will result in better balancing than setup 1, and provide the best overall low resistance. However, best balancing will be had with setup 2.