I am nearing the end of my degree (which is equivalent to a double major B.Sc in mathematics and physics) and the time has come to specialize in a field. The chliche is almost obvious, I am having a hard time choosing between studying:
I have not considered anything else. CS / engineering do sound nice and exciting, but I know too little about either to determine if I may enjoy them.
To make sure this isn't the standard "math vs physics" topic; I will attempt to detail as much as I can, and pose answerable questions.
After lengthy contemplation, I am still unable to realize towards where each academic degree would lead me. Academia is an option, but, adopting a more realistic point of view, the number of positions is small and I cannot foresee whether I will still like academia. This pushes me to explore other possibilities. Fortunately (or unfortunately) I have enjoyed both topics very much, and studied them with success.
To avoid unnecessary repetitions, in the rest of my post, physics would mean high-energy physics (phenomenology or theory). Math would mean geometry, functional analysis, probability.
I find this: MS degree after a PhD in physics demoralising, but would like to understand what I should expect. Expiriences like that probably answer some of my questions, and are very welcome.
As a preamble, I don't quite understand why you suggest that fundamental physics is connected to high energy physics since the bulk of recent foundational experiments have been done with lasers and atoms, but to each his/her own.
The large majority of physicists work in industry and do quite well, as you can see from the salary chart below (source).
Employment tends to be related to solid state technology, information technology or optical technology (the areas that produce the largest number of graduates) but even graduates in less industry-obvious specialities like high energy physics find industry jobs.
The running joke is that a physics and an engineering graduates are sitting next to each other at a graduation ceremony. The engineer is happy to get a degree, but the physicist replies that he (because there aren't that many female graduates) not only got a degree but also an education.
PhDs in physics have a capacity to reason abstractly and comfortably deal with the abstract. As a PhD candidate, you will have to learn a good deal of programming on various operating systems. You will be faced with challenges of data integration (or data fusion) and data interpretation, understanding filtering of data etc (especially true if you do high-energy phenomenology); these are but examples of a number of techniques that have wide direct industrial applications, irrespective of the field you specialize in.
Transitioning to industry is not necessarily hard, but you will not get an industry job because your thesis was on 10-dimensional supersymmetry: some flexibility is required.