I have visited different kinds of churches and Messianic synagogues, as well as Judaism synagogues. Probably the freest service is the Old style Orthodox. The men say their prayers, independently, and then might go outside and visit. For the Torah portion, and homily, everyone goes back in. If you want to go thru the prayers in a group, the cantor will lead the prayers, but you don't have to say them with the cantor.
I have visited Charismatic churches. You start with singing. Usually some fast songs, and then some slower songs during which a pause occurs while people pray in tongues and they wait for a prophesy. Then it stops, and another song. The announcements. And another song. then sermon.
Other churches have a program for the service. And others are liturgical.
Messianic services might start with the candle lighting if Friday. Then songs, and then the siddur.
I am pretty sure that God has figured out how to get done what He wants to get done in any order of service.
But, the truth is, I have seen more of God moving, outside of the service. Most of what God does, falls into signs and wonders, which is more for the lost then the saved, so it makes sense to me that more 'miracles' occur in a place which is visible to those who are not yet saved.