second router: access point vs. bridge mode

The answer to your question "does it give you something your current set up doesn't?" the answer to that strictly speaking is yes. as right now you need to use a Ethernet cable in-between the two routers with Wireless bridging you could set up the two to relay over a wi-fi link and thus no need to use a cable.

However if you got it working fine now and the Ethernet cable running between the two is not causing you any hassles then you won't really see any benefit with using wireless bridge mode over what you are currently doing. As a wired connection between the two will be generaly more stable, and faster then using a wi-fi link to connect the two routers which is the only new feature it offers.

End users, (the ones connecting to either router) will connect in the same way to their respective router in either setup. this new method only changes how the two routers talk to each other, and not to the computers that are connecting to them.