Django or Tornado?

It depends on ...

Project size

Django is a MVC (MTV) framework, while Tornado is just a basics needs to build a service (includes controller, simple templates processing engine and no ORM by default). Django has a strict well described project structure, and working with Tornado developers must to invent their own.
For bigger projects Django is a better choice because of easier code maintenance.

Testing

Django has its tests runner that makes writing and running tests smooth, especially if You use Django orm.
Testing asynchronous code in Tornado is a bit more complicated if to compare to ordinary synchronous code.
Be ready to spend some extra time on writing tests if You choose Tornado.

Project growth

When project is growing, we may need to extend team in order to support it; finding a developer who has experience with Django is much easier comparing to Tornado. Although Tornado is easy to start with, a new team member will need some time to get feeling comfortable with asynchronous code and new project structure.
Django uses a project structure that is proven by years of usage and allows to make project development easier.

Technology stack

Django has much bigger community comparing to Tornado. As a result, we have a lot of ready to use solutions, great documentation, huge knowledge base on StackOverflow and other resources.
Tornado works great when code runs asynchronously, but there is a big chance that library You want to use doesn't work asynchronously, so You'll need to search for alternatives or patch the library or write Your own.

Performance

Tornado works faster and requires less resources (if You use it properly).

Summary

If project is small, and we can make code works asynchronously - choose Tornado.
If project is big (You need more than month to rewrite it): split it into microservices (see Building Microservices book by Sam Newman) and select language/framework for each microservice that best suits it.

If a project is time driven: choose Django.