imho, high-level physics is harder than pure math. With math you can specialize and focus on some formulas or areas of interest, but this is not really possible with physics. With physics you have to know all the areas of math very well--group theory, differential equations, differential geometry, etc. You have to have know all the math well and all the physics from Maxwell and beyond. It's just much more material involved. To be on the frontier of physics is essentially pure math, plus hundreds of years of physics.
Computational Physics Ph.D. here...I don't know about that. I have written lots of code (not just using off-the-shelf packages) to solve Hamiltonian mechanics and Quantum reactive scattering. OMG, I spent about 30 minutes going through the Hamiltonian mechanics chapter from the point of view of a mathematician and I got lost about half way through. I feel like in my fairly long career I learned just enough of the math to make it work, but don't really understand the math at a fundamental level like I do the physics.
