For early music and especially with chant, no vibrato is necessary, and certainly no forced vibrato that becomes popular with opera. Church spaces are set up acoustically to let voices carry and echo, so a little goes a long way. In both recordings you can hear the strong reverb of the space.
But let's analyze the two example recordings you supplied.
When you listen to chant, keep in mind that in mass, Catholics are going to sing no matter what their voice sounds like. Allergies? Keep singing. Tightness in the throat? Keep singing. Dust and time affecting your voice? Never really got over that nasal thing from last year? Keep singing. Nobody here to hear you? Keep singing.
Now imagine it's 1995 and some one at the monastery in Luxumbourg borrowed some recording equipment. The chant has been around for eight hundred years, performed daily, reverently, by a constant stream of pious monks. So if it's Brother Maurice's turn to sing at mass and his voice is tight and stuffy that day, that's what going on the record, that's what going in the tourist gift shop.
Regina Caeli Chant
Now imagine it's 2006, the music industry is changed. The ipod has been out for five years and the iphone will be available in two. A music director at a very large church gets an opportunity to put together an album. She has access to musicians all over Chicagoland, including many that sing professionally, exclusively for the Catholic church.
The Chicago Archdiocese puts a big emphasis on providing beautiful music for masses. They're losing members and hemorrhaging money because they have too many buildings, and many of them are money pits. Traditional music, performed with some talent, is one of the few selling points they have.
Mary Gifford contracts Martin Pazdioch to sing for an album they can sell at a mark-up at the many religious shops around town. They want to compete with all the other spiritual/meditational music types that exist. Pazdioch will use the best of his talents to create music for meditation. His voice is clear and strong, with a little natural vibrato and subtle dynamics. Pazdioch is a music instructor. If his throat is tight or he's nose is backed-up, he's going to grab his flownase and do another take. Poor singing would be distracting to people who are used to modern music production, and they're not going to appreciate it on something that costs $29.99. The priests who manage the purses are suprisingly judgey.
so why are they different?
The Catholic church is presented in media in a variety of different ways, but the two big ones are
we come as we are, join us if you like
Our religion has given us talent and we're always this polished
Most music appreciators would prefer to hear the Regina Caeli, and say that this is authentic, accurate chant style. However, if you show up for almost any mass or service on a random Sunday, there's a good chance you'll hear something closer to the Credo, but it's not exactly on purpose. All over the globe, in places big and small, Pastors have to sing, in public, every week, no matter what. Some will be great, some will be just be good, but to judge them on their singing talent would be disrespectful. Their talent and goal is worship above all else.
This is a long winded way of saying that I don't think the Credo was sung in a style that's particularly different or special to chant. He's singing through his nose, which means he's in the process of getting some vocal training and hasn't reached the point yet where the singer integrates head and chest voice, or he's holding back a sneeze, or this is just how he sings. The recording is fuzzy, which means this was probably a recording of an actual service. If that's the case, then it was recorded to capture the real sound of the monks in service, allergies and all.