I say don't use the bevel. At all. Instead:
1. Press plus (numpad "+") to work in subdivision mode from the get go. (Times 2 if your computer can cope with it).
2. For the working viewport, go to the Camera Visibility (shift + S) > Attributes tab and turn on Polymesh hulls
3. Goto shaded mode.
5. What defines the sharpness of the sub-d models edge is the distance the second edge or "inner" edge is to outer edge. So in the image above you can see that in the lower viewport, the left side has a second/inner edge causing a tighter curve while the right side is much softer.
6. With this technique using inset on an single polygon can have a similar result as using bevel. However, I recommend just using split edge and subdivide edges evenly.