Segment Pro is rules based and limits a bit of what you can do to individual rings. WTP gives you full control of each ring including the base.
In SP a way to make the bottom disk larger is in the BOWL Settings window, bottom right side you can use the Diameter less / more buttons.
- By clicking on the button, the vessel diameter will be decreased / increased including the base disk.
Another way is in the Profile View is to mouse over the "red dot" at the base, hold down the mouse button and move the dot.
That will change the profile.
Not sure why you are wanting to change the size of the base disk if the rest of the profile is fine.
The last alternative is to build the vessel in WTP. You can input what size you want the base to be, (diameter and thickness).