In my honest opinion, the most beautiful church in Buenos Aires is not the national cathedral but this basilica in Almagro. To rely heavily on cliche, it’s breathtaking. Stand in the center and do a 360, taking in the entire ceiling and organ in the back.
It also has hosted two of the city’s most important citizens: Jorge Mario Bergoglio (a.k.a. Pope Francis) was baptized here and a young Carlos Gardel sang in its choir.
The basilica was built in less than 10 years with construction ending in 1910 and is the largest architectural work of the Salesianos of Don Bosco in Buenos Aires.
Important: Opening hours can be difficult to keep track of, check their Facebook page before visiting. During the week they typically close from noon to 4 pm. On Mondays, they open only in the evening. Weekend hours change. Always check before going, I've had the doors closed in my face (apologetically) when I arrived 5 minutes before closing time.