Surely there is also the factor at which level the weapons were used. For instance the standard British divisional gun was the 25pdr, anything bigger was held and used at the Corps level, with the rider that a British divisional artillery observer could call the corps fires of hell down on a suitable target.
The US used a mix of 105mm and 155mm howitzers (well, even though not admitted, the 105mm was a gun-howitzer, like the 25pdr) at the divisional level. Again with 155mm guns and above (well as the 155mm gun had a two stage propellant load so in some ways it could also be strictly considered as a gun howitzer).
So what were the German equivalents in terms of divisional and corps artillery? Divisional artillery needed shorter range. Meanwhile, as far as I read, German divisional artillery started with 7.5 cm guns, then went to 10cm howitzers, then back to 7.5cm guns.
Some German divisions had artillery of both 10cm and 15cm, so would not have required corps level range.
At Barbarossa most frontline Divisions had three battalions of 105mm and one of 150mm (12 guns each) but lower priority Divisions might only have one arty battalion. The Divisional artillery had as its primary task to support the combat of the Division and had its fire closely coordinated with the movement elements of the Division. If the ideal frontal coverage of a Division of 10-15 km could be kept a range of 10 km was enough to have all or most of the Divisional artillery support in all of the sector but German Divisions soon found themselves covering much larger sectors and outranged by the Russian artillery at all levels. In moving combat a shorter range also means that the batteries have to spend much more time on the roads instead of in firings positions to keep up with the combat, no matter if you go forward or backwards, but at a time the extra range is paid for too dearly by too heavy pieces being too cumbersome to move.
IMHO the German 105mm lFH 18 found a good balance between range (10 km, but eventually 12+ km with muzzle brake) and weight (2 tons) but a piece weighing almost 6 tons and ranging less than 10 km appear out of balance - especially if you have limited access to motor vehicles. For all the effort put into the sFH 18 it would have appeared more beneficial to take the barrel from the old sFH 16 and put it on a new split trail carriage (was done on other WWI origin pieces). That would have provided a piece with only marginally shorter range but at less than half the weight - ie. realistically to be towed by horses or by lighter motor vehicles.
At Corps or higher level you basically had two types of fire support. One was quite heavy (6-25 tons) but long ranging field guns to engage targets in depth like enemy batteries, HQs or junctions. An example was the 105 mm sK 18, which used the same carriage as the sFH 18 but instead of the 27 caliber 150 mm barrel had a 46 caliber 105 mm barrel sending a 15 kg shell out to 16 km, and in a later version to 19 km. The later was sufficient but compared bad to Russian pieces like the 122 mm A-19 which from the start of the war sent a 25 kg shell out to 20 km. It did weigh almost 8 tons, but with that range and reasonable Russian access to heavy tractors that wasn't a big problem.
Around WWI medium and heavy field guns usually had to be transported with barrel and carriage separated, but interwar designs usually "just" had to wind back the barrel and fix the breech end at some point on the trail for transport. But it still made these guns very cumbersome and vulnerable to counter battery fire.
The other task of Corps and higher level arty was simply massing fire for the supported unit. This was an effective way for the Corps or Army commander to focus his effort (set "Schwerpunkt") in both defensive and offensive operations, and as mainly howitzers and rocket launchers were used in this role you could relatively easy shift the "Schwerpunkt" - providing the ammo probably was the biggest challenge. The sFH 18 was used in this role (not much else was available) but was even less suited here than for the Divisional role.
Th Germans never had enough guns (or ammo) to mass fire like the Red Army but relied more on flexibility - although never could match the British and Americans in the "flexibility game" - I guess never having as many reliable radio sets was an important factor.