I use 0.2mm, 0.4mm and 0.8mm radius inserts. The 0.4mm inserts get used most for general turning and the radius is a good compromise when a really sharp internal corner is not needed. I use the 0.2mm inserts for smaller diameter work and where a sharp internal corner is needed. The 0.8mm inserts are used for heavy roughing, especially in steel and cast iron, and where I want a nice fillet.
To some extent the smaller the insert radius the smaller the final depth of cut can be and still maintain a decent finish, although many other factors also need to be considered. Similarly the larger the radius the higher the feedrate can be for a given finish, which may help with chatter problems. Speaking of which I've never had a chatter problem due to the 0.8mm radius inserts, but I do drive them fairly hard.
While I find it useful to have all three options available the 0.4mm insert is a good compromise.
Andrew