I use MailPoet for a general mailing list, and it works very well. I especially like the close integration with WordPress that allows me to have automatic post notification emails go through MailPoet. I have not explored switching to Church Admin for post notifications because this setup works well for all involved.
I also have the MailPoet plugin set to override WordPress mail functions and instead send mail through the MailPoet Sending Service. My Church Admin emails are being sent this way. This has some limitations over the header of the email (specifically, the from address and reply-to address are not changeable), but it has been working for our purposes.