Which Fortran method? Is this equation stiff? If it’s stiff then you shouldn’t be using Vern9 and would expect this kind of difference.
Are you sure the model is implemented correctly? Plot the output and double check that it is the same. Most of the Fortran solvers have a wrapper, so you can just call for example solve(prob,radau()) and see if the values are exactly the same between the Julia and Fortran version.