Java applet or a custom browser plugin?
The universal API for browser addons is javascript. It is well supported in Firefox, Chromium/Chrome, and Opera at least; it is the only extension API available on the last two. Intersting API subsets are firefox's Fuel, Chromium's trimmed down extension api, and the very portable GreaseMonkey functions.
A second runtime would have its own startup costs, garbage heap, and ffi overhead. It would require special privileges, and would still have to translate its API calls into javascript. That would make it fairly unattractive.
Edit: you were asking about web content with possible plugin or addon support? You also have the option of the NPAPI (also the Pepper project around it). This api is C-level and can render to a rectangular area on its own (using OS APIs), at the cost of very little support from the browser and being a portability nightmare.
We're writing a platform for building apps that are able to run on any browser and we were thinking, is there a way to do this with Python? Or should we better go with Java and Java Applets? 
I was also wondering, how hard is it to write a custom browser plugin? How long would it take e.g. in man-hours? 
Thank you!