Other than the cruxifix on the wall and a prayer at graduation, you could stay completely oblivious of the Duquesne's Catholic nature. They did cancel classes for 2 hours for a mass for the pope when he died, but that was a big event, and of course no one was required to go.
There is a healthy mix of liberal to conservative in the student body and with the profs. I have to say I trully love my experience. My classmates are on the whole are smart and hardworking. People are generous, no one is going to hide a book or steer you astray, they are likely to share their outline.
First year writing program is a bit uneven. You could get an incredible prof or a mediorce one. (mine was law review editor at Harvard, so I was happy even as my ass was being kicked). The curriculum has a lot of required courses- to prepare you to take the PA bar. So if you like lots of electives and the bar you want to take is not PA or a bar that tests similar things, then you may not like that. Personally I had more than enough room in my scedule to take the classes I wanted and I had a fabulous trip to Rome through the school last summer.
Job prospects are good regionally. So a Duquesne degree is best if you want to practice in PA. I have a summer associateship with a big firm, so oppurtunities are there.
All things being equal, I'd say if you want to practice in NY- Albany is a great choice. If you want to practice in PA, then don't worry about Duquesne being Catholic. You won't even notice unless you wanted to to start a lawyers for choice group on campus.