Bigger is not always better.
Your old pump was sized properly to deliver the required GPM and pressure within the operating parameters of the irrigation system requirements. You new pump produces higher pressures and GPM volume thus, it is able to reach shutoff point of the pressure switch. This cycling will kill you in energy costs starting the motor so many times, besides wear it out quickly.
A tank may help but will most likely just slow down the frequency of cycles. Many things can be done such as trim the impeller, add more zone demand to increase flow requirements, install or use a balance valve to decrease flow at pump outlet/inlet or a combination of all these that would work best.