Having visited the one in Paris first, I'm impressed how similar this version is to its namesake. The architecture is much less ornate, but the interior decoration is similar.
Tourists can attend mass for free even if they aren't catholic. It was about an hour and absolutely awe-inspiring. The priest spoke four languages and the massive organ in the back was INTENSE.
I think hearing the music and benedictions in a place like this is a better experience than even getting a guided tour, because you can read about all the facts later anyway. Just don't take communion if you aren't supposed to, obviously, because that's disrespectful.