Is it more accurate to capture the pulses on the rise as opposed to when they are falling? What is the advantage to change that portion of the code?
It really depends on the sensor. Most hall-sensor type I've dealt with are active high which means its best to capture pulses on the RISING EDGE. Now if your sensor is active low, then you capture on the falling edge.
TCCR1B = 1<<CS12 | 1<<CS11 | 1<<CS10 <------------ this captures RISING EDGE
TCCR1B = 1<<CS12 | 1<<CS11 | 0<<CS10 <------------ this captures FALLING EDGE
These
bitSet(TCCR1B, CS12); // start counting pulses
bitSet(TCCR1B, CS11); // Clock on rising edge
are equivalent to the latter (capture FALLING EDGE)