The answer to this is not always the same. There will be some messages whose contents are more important than the way in which they are delivered. There will be some for which the opposite is true. It is also the case that different receivers of the messages will feel differently about what is important.
Just as not all people send communications in the same way, not all people receive them in the same way. There are some people for whom nonverbal communications are more important. These are people who are more oriented to nonverbal cues than they are to words. Other people will only hear the words and will not care so much about the delivery.
Perhaps more importantly, the answer to this can vary with the message being sent. For example, if someone tells you that your spouse has died, the nonverbal aspect of the message is not likely to matter very much. The content of the message will be so overwhelmingly important that the delivery will be largely lost to you. For other messages, the delivery can be more important. For example, if you say something like “tell me more” to a friend who is talking about their troubles, the way in which you say it can mean much more than the actual words. If you are leaning forward and attending to them, your message will be very different than if you are playing with your phone and you sound distracted.
Thus, the answer to this question will vary depending on the message that is being sent and on the personal characteristics of the person receiving the message.