Do you have a traditional and a contemporary service with separate teams for each?

Get your teams together! Have a team gathering with everyone that serves in BOTH services.

See, right now it's likely that there are two cultures, each with their own strengths and weaknesses.

Have one group appeal to the other in terms of values. 

For example, the traditional service folks "just show up every week and sing the hymns they've always sung...and are always punctual." Translation: they are extremely faithful and committed! Have them share with the other team (who tends to arrive late) those values.

And perhaps the contemporary team is more open to a variety of styles and are good about honoring people that don't share the same style preferences. Translation: they can teach about honor.

Can you picture this? 

It's like Martin Smith said back in the day "when all the streams flow as one river to wash away our brokenness!" #DidYouFeelTheMountainsTremble