I was thinking of simulating a cyclotron using GATE as a platform and I was wondering if it's the correct platform to use or is it better to use another platform (Geant4 for example).
Can you be more specific with what aspect you'd like to study? Several codes are capable of simulating particle transport in general and within electromagnetic fields, e.g. PHITS, MCNP, and GEANT4. In general, PHITS and MCNP are much more user friendly than GEANT4. Do you just want to simulate the beam? Interaction with target material (nuclear reaction/energy deposition/etc.)? Motion of particles within the cyclotron/related components?
Actually I don’t want to simulate the whole cyclotron. I want to focus on the output beam and it's interaction with the target material ("nuclear reaction, energy deposition..").
PHITS is my preferred platform for these types of calculations: https://phits.jaea.go.jp/index.html -- it is simultaneously very powerful, versatile, user-friendly (easy to install/run, and no programming knowledge required), and the manual/documentation is replete with examples describing how to set up these types of calculations.