In terms of carbon emissions you'd need the flights to be long, and the trains to be pretty inefficient and empty (think current Amtrak trains), and even then there is evidence that the high altitude appears to make the emissions significantly more harmful than the equivalent ground-level emissions
Isn't flying the most expensive kind of transportation ? Plus it relies on fossil fuels big-time.
I'd love a high-speed rail from Vancouver BC to Calgary Alberta, or Prince George (both places I go every year). But building such a structure is a monumental task (10s of billions) and a fast train would take a vast amount of energy covering that distance. Imho trains just cannot compete in such markets.
I take the train everyday. For me, travelling by train for < 4h trips to a city sounds like a good deal.
It is generaly a smoother experience than taking a low-cost flight. But, I realize it really depends on how 'car-first' and large your country is. Definately not an universal solution.
I'd have to see the math, but there is also a question as to carbon emissions per-passenger/distance. I believe that on long flights (more time at high altitude) widebody aircraft might be more fuel efficient than high-speed trains stuck on tracks.