Most electronics use micro-controllers like an AVR, but I'm seeing ARM chips in new electronics. ARM chips are said to be more powerful, but in what areas related to 3D printing could this help? What are the features that the AVR struggles with and where an ARM could be better?
High Speed movement? Delta printers? Graphic display?
And is the AVR really the limitation there?
Generally, AVR is in fact less powerful than many ARM cores used today. Most printers with AVRs don't have floating-point coprocessors, although a lot of the step and movement control can be done in integer-only math (except for G2/G3). Marlin can interrupt for step handling up to 10000 times per second on AVR, translating to 40000 steps per second. This isn't particularly useful without mechanical components that can move at those speeds and still print meaningful results (or are far more precise and have a far higher step-count-per-mm at a similar speed).
Graphic display isn't a particularly taxing thing to do at low speeds--high speeds or weird interfaces might require a bit more power or a dedicated interrupt.
The times when ARM might be important are for more math-heavy and especially floating-point-heavy setups such as delta, where every move requires many floating-point and trig operations, and navigation in menus on a 16MHz AVR (atmega2560) is described as "painfully slow", but Marlin does succeed in printing meaningful results on delta-style printers.
Clearly, an ARM core that is either faster at performing soft floating-point, or supports hardfloat (hardware that does floating point operations very efficiently) will see a benefit for such processes.