The two churches I play at don't split the difference. At one, we have a P&W section that has the full choir participating. Sometimes it's a smoothly arranged, well rehearsed contemporary set. Other times it's a spontaneous "let's get the congregation singin' 'Jesus On The Mainline' " type of thing.
The "choir songs" are focused around the formal parts of the service...Call To Worship, Invitational, Offeratory, et cetera.
At the other church, in theory there is no "P&W Team", there's just a choir. Three choirs, actually, that rotate based on what Sunday it is. On 4th Sunday, I'm responsible for the music and it gets as close to P&W as this particular church has ever witnessed. I say that based on song selection, which tends to be more contemporary(Hez, Fred, John P.Kee, Donnie, etc), whereas one of the choirs is more focused on anthems and hymnal songs and the Men's Chorus tends to do spirituals and quartet type stuff.