For use as a general-purpose OS and application drive, write speeds are almost irrelevant. The huge majority of accesses are read accesses.
The big advantage of an SSD is it's very fast access times (which are different than transfer rates). They allow the SSD to find lots and lots of files very quickly. This means that a system with the OS and applications on an SSD boots and starts applications much more quickly.
But once an application is up and running, whether or not an SSD helps depends entirely on the application. Some applications don't do much disk I/O as they run, and for those an SSD won't make them run any faster once they're loaded.
Web browsers do tend to deal with lots of little files because web pages usually consist of many files and because the browser caches everything on disk. So an SSD can speed it up (as long as it's using the SSD for its temporary storage).