The short answer is that both are good for different applications. Each has its pluses and minuses:
Price ACME is typically less expensive, even in multiple start systems.
Maximum travel R&P is required for longer axes. The main reason for this is that screw-driven systems are susceptible to “screw whip”, which is an off-axis motion that worsens the faster a screw rotates. For ½” screws (even multiple start screws, which fare much better due to their higher ratio of linear travel per rotation), the critical speed of rotation makes axes much over 4’ in length impractical. Larger diameter screws can be used, but since rotational inertia is a function of diameter squared, much larger motors are then required to achieve acceptable speeds.
This is where R&P really shines. The system can be used to create axes of arbitrary length, limited only by the length of the linear rail guiding the system. Racks are typically available in 6’ and 12’ sections, and if necessary can be spliced to create extremely long travels. The fixed cost of the drive system and the relatively low cost of cold rolled steel and gear rack make the cost per foot of travel highly competitive for larger travels.
Accuracy Many people assume ACME is more accurate than R&P, as a screw drive typically has more resolution than our R&P units. Indeed, in theory, a ½-10 single start ACME screw paired with a 10x microstep driver will have an effective resolution of 0.0001”, whereas our Nema 23 R&P with the same driver has an effective resolution of around 0.0005”. However, both of these resolutions are more than adequate for large format cutting, and inaccuracies at other points in the system (such as screw lead error and backlash) make these differences more or less irrelevant.
Speed There is an appreciable difference in speed between the systems due to gearing. The R&P is geared more aggressively to better utilize the low-end torque of stepper motors, and is also more mechanically efficient than ACME screw systems. Because of this, it is capable of much higher top speeds (rapids of 600 IPM+ for some Nema 23 systems and 1000 IPM+ for Nema 34 systems) than even multi-start ACME. That being said, for shorter travels, this higher speed is rarely realized, as there is insufficient room to accelerate to these speeds, so in this case, ACME can be a good and economical choice.
Other Considerations R&P systems do have a moving motor, and hence require more cable management than an ACME axis, which typically can have at least one stationary motor. Another consideration is that it is difficult (albeit not impossible) to do a center mount R&P unit, so most R&P systems are dual drive on the long axis. Lastly, for z axes, R&P is not really appropriate, as it can be easily back-driven when the power is off, and can cause the axis to fall in an uncontrolled fashion. This can be controlled with a gas spring or other apparatus, but the cost and complexity is rarely worth it.
Summary Choose R&P for axes that are 4' or greater in length, or for an axis you might want to upgrade in length later on -- it will be faster and will alleviate trouble with whip. For shorter axes, choose multi-start ACME to save cost.