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The answer is in the effort and the nature of relationship.
Customer Relationship Management is Proactive and Customer Managed Relationship is more of Reactive.
You put in the efforts into Customer Relationship Management while it is the customer who is taking the initiative in a Customer Managed Relationship.
CRM is always better than CMR.
But there would definetely be time when you have to deal with CMR.
You will need to remember that a CMR is a rsult of a failed CRM.
If and when you see a CMR emerging - grab the opportunity and reach out to this customer and rebuild the relationship. All the best.