I reached that by accident. Service B for DNS was just a more pleasant product to use than service A, and service A didn't offer certain features I needed for emails.
To bring it back on topic, this made it easy when I switched service A from Gandi to something else a year or two ago because a few things I was seeing from them "smelled funny." I don't remember the details, just that I wanted to switch.
DNSControl[1] or another similar tool also helps a lot when moving. My DNS records are configured by a small JavaScript file in a git repository, and I can very easily point it at another DNS provider.
