This question comes up quite frequently among Worship leaders, and here's my take on the issue:
The answer is “Yes”.
“Don't be such a smart-aleck,” you say, “Pick one.”
Well, here's the difference: some songs the congregation is not expected to sing along with (e.g the one during offering, and often the first one of the service). They are designed to be listened to, kind of like a mini musical sermon. For songs like this, the “performance” aspect is more emphasized, because things like loud versus soft, solo voice versus harmonies, emotional content, etc. help convey the intent of the writer, and/or the interpretation of the performer(s). Because these songs are meant to have some kind of spiritual message, being able to hear the words is also important, so I try very hard to make sure they are not obscured by an off singing style, weird pronunciations, too much instrumentation, as you very often hear in secular pop and rock music.
Other songs are designed to be primarily sung along with. We often call these “worship songs”. We used to call them “hymns”, but that's reserved for the older songs now ;). Note that the "performance" type of song can be worship, too (listening and absorbing the message of it), just as a worship song or hymn can be made into a performance piece.
For worship songs, the “performance” aspect is diminished, although you can hear worship leaders all over the spectrum. An audience (congregation) that is almost all young teens or adults is willing to let the performer(s) take great liberties with the melody, improvise a lot, and sing in a key that is geared to young voices and tastes. A typical church, though has people of all ages and types, so my personal feeling is that the worship team should stick to the song's melody with hardly any departures. The key should be one that the most people can sing in, even if that means a bit of discomfort for the team. The lyrics should be very easy to pick out, not being obscured by instrumentation. I believe there is room for some “performance”, though. Dynamics of volume can help convey the intent of the song. Adding harmonies can help make the song enjoyable (and some people in the audience might actually prefer singing the harmony instead of the melody!) A little improvisation by an instrumentalist or the lead singer can also help convey meaning and emotion.