Why I use MailChimp for myself, and my clients
I recommend that small law firms use MailChimp as its paid plans that offer marketing automation are highly affordable. Also, most small firms have e-email databases that are too small to justify paying for more sophisticated functionalities of other marketing automation vendors. Lead nurturing campaigns are simpler to implement when your database is small. Similarly, smaller and less complex campaigns can be tracked and monitored manually, and the data generated can be sufficient to inform your decisions as regards refining and improving your marketing programs.
If, however, your book of business and your e-mail database are so large as to require contact segmentation and consequently separate lead nurturing programs, you may want to look into the bigger service providers (e.g. Infusionsoft) that offer more integrated tracking and reporting. But if your e-mail database is just getting built, or you don't have different types of content to cater to different categories of subscribers, my recommendation would be for you to stay with a basic provider such as Mailchimp.
There are many players in the automated marketing sphere today. I cannot speak to all of them. But I tend to go for what works (and what I use myself), and then scale out when necessary, rather than paying for all the bells and whistles I do not yet need. The money I save can be put to other more productive uses, such as secondary or related marketing initiatives.