My question here is, would the decreased bit-count as well as the lower processor speed really matter to us? [...] So, main differences between an 8-bit 16MHz AVR microprocessor and a 32-bit 72MHz ARM Cortex-M3 microprocessor?
What a cool project! This is a great opportunity to learn a bit about how processors work and what bit-width and clock speed mean.
Clock speed is conceptually the easiest to understand. Microcontrollers like the AVR and ARM use a clock crystal that sets the speed the circuitry operates at. With a faster clock, the processor can execute more instructions in the same amount of time. The 72MHz clock is more than 4x the 16MHz one, so the ARM processor is going to be able to run 4x faster than the AVR. But what does "run faster" really mean? Processors execute instructions. At the basic level, these are instructions like "add two numbers" and "make the voltage on this pin high". The ARM processor is going to be a lot faster here, but consider what hardware it's going to be talking to: servos. Servo motors listen to a fairly low-speed PWM signal, so at that speed the difference between 72MHz and 16MHz isn't going to become that relevant.
But what about bit-width? This one is a bit more tricky. It doesn't really affect the speed at which your processor runs, but it affects the complexity of the instructions it executes. Let's say that you want to add two really big numbers together. Numbers like 100,000 and 200,000. When we add those together on paper, it's just one step. But an 8-bit processor like the AVR can only operate on numbers as large as 65,536. So in order to operate on numbers that large it'll need to break up the addition into several smaller steps. The 32-bit ARM, on the other hand, can work on numbers that large. So it does the addition in one step. I hope that makes sense.
Anyway, I've done a lot of work with servos on even slower processors than your 16MHz AVR. It'll most likely be just fine for what you want to do, and like you found it has a much more active hobbyist community. And if you're looking for quick examples of code, the Cornell 4760 page has some great projects that you could learn from.