Work: Python/flask with gunicorn and nginx, postgres for relational (90% of the time), mongo or Cassandra for document store, jQuery, sass, gulp, puppet for config mgmt, centos 7.2.
Personal: mostly the same except Mac osx or heroku for host, and no config mgmt.
All great questions. I haven't done any genuine analysis outside of "this seems fine on my MacBook" which I fully admit is not worth much.
Check out the example app and endpoints app, then load the poorly.json and kitchen sink.json files into a new dashboard. I wouldn't expect anyone to make dashboards that extreme and they all render fine (we're talking upwards of 30 charts, many using webgl for 3d).
All that being said, I will continue to make this more optimized as I can.
We use flask backed by apache mod_wsgi running in containers or VMs at work for our micro Services and it's quite performant. I've run stress tests with this setup using freeBSDs siege command (awesome btw) and 1000+ concurrency and it ran without a hiccup.
I can't say at what level it would break, but I'm confident it would perform as well as django (and it's designed to be thread safe so assuming your following the 12factor app principles And use the process model/attached storage for persistence running elsewhere, you can run multiple threads, apache vhost multi threading notwithstanding.
Personal: mostly the same except Mac osx or heroku for host, and no config mgmt.