By accuracy I mean it hits what you're aiming at, as close as possible, with the first round, and the MPI of subsequent rounds. This has a lot to do with the stability of the carriage and the recoil system, as well as the fire control system to maintain that point of aim.
Consistency is the ability to continue to hit near that same spot, in a sense "to have a tight grouping". The factors affecting accuracy affect this too, but consistency of ammunition manufacture and stability in storage plays a big part as well
The M777 is inherently more accurate than the M109 first because of the recoil and carriage design. The recoil pistons are pushing in towards the trunnions, shortening the length of pull, as opposed to the M109 which is pulling out and away from the trunnions and increasing the force the further it is pulling from them. The recoiling parts of the M777 are pushing in towards a more stable area of the carriage; between the trunions and low down. The drawback is that the breech is far enough forward in the carriage that it needs an hydraulically assisted breech operating and loading tray system, making it a bit more complicated compared to some towed guns.
The M777 carriage is low to the ground and rigid, which is not such a plus on unevenground, but lends to greater stability; once in-bedded it is not moving around.
Optic laying systems are about even between the M109 and M777, but the vagaries in the traversing mech of an old M109, also contending with the mass of the cab (turret) are going to be a bit more than those of the M777 dealing with a much smaller mass to keep still once laid and dealing with the stresses of firing.
As far as displacement goes, time permitting, the spades of the M777 should be dug in, if they're not it certainly can displace backwards quite a distance if a high charge is fired at a relatively low angle. (yes to those from A Bty reading this I remember Dec 05 when a gun did displace off a small knoll sliding back and downhill +20 Metres, but this is why we got the jack hammers as part of the kit to dig the spades in.) In winter conditions the M777 might have a problem with displacement that the M109 wouldn't, but only if time didn't permit the digging in of the spades. This can be mitigated, again, by using lower charges. In the case of the digital system it doesn't matter since the ring laser gyro of the INU isn't affected by this displacement, it will continue to give accurate laying data relative to the data sent. The gun would have to displace a considerable amount before the original QE from the CP is no longer valid, in which case the gun would have to send set up data again and the data recalculated, but keep in mind this would require the guns to be firing at a very high charge at around 300 mils, and that really isn't necessary, so why do it? A high charge is not necessary not even for direct fire, the gun is very accurate even at relatively low charges. I realise this is contrary to the long practiced habit of using the highest charge possible during direct fire, but not only is it unnecessary, it is verboten in most cases. Even in loose sand firing a low charge will reduce the displacement considerably. I recall the US NETT in Ft Sill mentioning that the picture taken with the spades digging away (I think "Guns" uses this as an ID photo) was done at a very high charge to show what could happen. You shouldn't let that lead you to believe the gun ordinarily pushes back like that every time or even with the 1st round.
The Modular Artillery Charge (MAC) high comes in two different brands, M232 and M232A1. M232 was part of the Crusader program and burns hotter (IIRC it is a double base propellant) than the triple base M232A1 propellant. M232 shouldn't normally be used in the M777 but has shown up in theatre and was used, no biggy, just that it causes more wear than the M232A1 (BTW the crusader had a chromed barrel and cooling jacket to deal with the higher temperature). M232A1 will have more area under the pressure curve but will peak later relative to say M119 (red bag) and M4A2 (white bag) type of propellants; it has more push. The manufacture and stability of this propellant is what gives the M777 its greater consistency relative to the M109, plus the stability of the carriage. The more current M109s , like Paladin, with a M777 barrel (not the gun, the M777 has a M776 barrel, just to confuse things more) can fire the same ammunition as the M777, but our old M109's have the old M185 tube, and it is not designed to take the range of ammunition that the M777 can, in particular MAC high, there is a MAC low M231 that it might, but not sure how well it would hold up with that either, but as far as I know it hasn't even been modeled let alone tested for MAC low anyway.
The return of our old M109's is only being considered because there are still parts available for it, not all were disposed, and given the high cost of current Ops and other priorities, I suspect there is a possibility they will be brought out as an interim measure until a clear replacement is identified and funded. In the meanwhile there are 3 Regular Force gun Bty's out there with borrowed or no guns.
In the for whatever its worth dept, IMHO, I think the M777 should eventually permanently replace the LG1's, the light Bty keep the mortar but the infantry should stand their Mort Pl's back up too (although given current priorities and manpower shortages I doubt that'll happen, but just an idea anyway). The other gun Bty needs something, and it ain't the C3, don't know what yet, who does? The 3rd Bty is the STA Bty. In reality it seems to be a moot point since the Regt's can man just 1 gun Bty, the STA requirement, and some HQ now as it is.
Ok I'm drifting here, better stop, but...
Did I cover everything?