It's hard to compare price because it is very rare for two means to compete directly. It's often apples and oranges. A train that moved as fast as plane isn't going to be very fuel efficient. They can be electric (insert source debate) but planes can also run on biofuel (another debate). And when comparing plane-train, a plane burns much of its fuel taking off and climbing to altitude. Once there (10,000m) it is remarkably fuel efficient in terms of passenger/mile at a given speed. And there are times when rail simply won't ever be an option (over large water). The head of RyanAir gave a great presentation a couple years ago about highspeed rail. His point was that, while great if you live in london and vacation in Paris, most people don't live downtown, that planes can land in places much closer to actual destinations --> reducing total-journey emissions.

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.