If you need your emails to be sent in a time-sensitive manner, I'd recommend SendGrid. We were using Mailgun and the lag because they aren't "transactional" in nature caused issues for us. SendGrid also has the ability to do dynamic templates and bulk send from their API. I don't know that they have the shared layout ability you mentioned, though.

The only transactional email service that I've been able to stomach is Postmark! It is by far the easiest (and quickest to get feedback from) service that I have come across. While drowning in attempts to debug Mandril, Mailgun and others I get quick feedback from Postmark in what I need to do.

Postmark for the win!

We are using more extensively Mandrill.

It is a ok tool, which gives you the power for emailing with nice set of features.

The templates editing and management is a bit tricky, but this is mostly related to email templates in general, which are hard to create and maintain.

I do not think you can share the parts of the templates. You can have your predefined templates with possibility to insert dynamic content.

They provide a limited possibility to preview and test your templates.

The template editor is text only. For the better editors checkout http://topol.io or https://mosaico.io

Unfortunately, I do not have experience with the other tools and possibilities to manage templates.

At this stage, all of the tools you mentioned do email delivery pretty well. They all support email templates as well. Here are some considerations:

1. Twilio owns SendGrid. If you're an existing Twilio customer, in my opinion that's a good reason to use SendGrid over the other solutions. The APIs are solid, and Twilio has excellent developer tools that allow you to create interesting automations (which is important for scaling).
2. Mandrill was created by MailChimp, who have massive experience with email delivery and specifically with emailing beautiful email templates.
3. Mailgun is a tool on its own. Like the other two, it supports mail templates and is built to be controlled almost exclusively via APIs.

SendGrid and Mandrill have pretty nice WYSIWIG template editors as part of their platform. Not so sure about Mailgun.

So for me the considerations would be: 1. How easy is it for you to integrate with their API? How complete is their API in terms of your own specific needs? 2. Prices: Which one works best for my budget? 3. Am I OK with editing the templates elsewhere (or even by hand), and then pasting the code into Mailgun? Or do I want the comfort of Mandrill or Sendgrid with their WYSIWYG editors?

Personally I'd go with Twilio, simply because it's such a massive ecosystem they are less likely to go bankrupt, and their APIs are rock solid.