I would like to discuss about the impact of the weight of the gantry on the mouvement of a screw/bolt driven machine. While this impact seems to me obvious in the case of the belt driven machine, I have a doubt if this is similar in case o screw driven, as far as the screw/nut mecanism is not reversible : I mean, pushing on the gantry will not make the nut to rotate (BTW, I am using regular threaded screw, not ACME). What do you think about this ?
Force = Mass X Acceleration
Regardless of how you move the gantry (i.e belt or screw), the force required to accelerate it will be the same; the heavier (i.e. the greater the mass) of the gantry the greater the force required to get it up to speed. Once up to speed the force required to keep a heavy gantry moving may not be much greater then a lighter one; it depends on the type of bearings used. And, of course in the case of a cnc router, there's also the cutting force to be taken into consideration.
Lead-screws with fixed nuts are rather inefficient at turning rotary motion into linear force; they require about as much force to turn them (radially) as they produce long-ways (axially). That's why you cannot rotate normal screw threads by pushing on the nut; the friction you generate by pushing the nut against the thread is greater than the turning force you are creating at the same time. The efficiency of the thread is dependant on the design of the thread; pitch, profile shape etc. The friction will vary with the material of the thread, nut, and the amount of force pushing the two together.
Belts are considerably more efficient than screws at converting rotary motion into linear motion (that's why you can often back-drive them).
So, the impact of gantry weight, or more correctly Mass, on the screw/fixed nut driven system is actually greater than the belt drive (or ball screw, roller-nut) design. However, since friction is usually high in a lead-screw/fixed nut design, unless your gantry is truly massive, the impact of the acceleration forces may not be noticeable.