From the startup time to searching to drafting/sending a message, the UI feels comparatively slow relative to using Gmail.
One idea is to have a 'slim' draft message option; the idea being if I have Thunderbird set as my default email client and I click on an email link in Firefox (and Thunderbird is not open), I have to wait several seconds (10+) for the whole app to load before starting to draft my message.
Another pain point is navigating filters and search within the app - even a loading screen while waiting for search results to load, or having other docs for reducing the size of your mailbox.
I think because everything is local, latency/snapiness is one of the key factors that Thunderbird should have over a web-first email client.