For those coming behind, and contemplating a saw purchase, get a circular saw.
On my cabinet, there were only TWO cuts that I couldn't make with a circular saw, using a metal saw guide to keep them nice and straight.
(You can substitute the uncut edge of a piece of MDF or plywood in a pinch).
Those two cuts were both small inside-curving cuts, so I used a jigsaw on them.
Had I been on a budget, I would have bought a coping saw, cut them as close as possible with the circular saw, and used that to finish them off.
Even on a perfectly maintained jigsaw, there is usually some blade deflection.
There just isn't enough meat on the blade to keep it from bending.
For outside curves, you can trim them down as close as possible with the circular saw, and then sand them to your "cut" line.