There seem to have been three ways people thought of to improve the performance of the original T-Gewehr.
1. Jack up the velocity.
2. Whomp up the calibre.
3. Use something other than steel in the penetrating core.
Different nations plumped for different choices.
The Poles went for 1 and 3, with the odd choice of lead as the core material, and the use of a highly efficient muzzle brake making a nice light weapon.
The Germans went for 1 and 3, with a more conventional choice of tungsten carbide for the penetrating core, but with a bit of a pointless and legally dodgy diversion into adding a tear-gas carrying pellet to increase behind-armour effect, which it didn’t.
Having first experimented with the deliciously strange Kurchevsky 37mm recoilless anti-tank rifle, the Soviets chose 1. They did not reduce the calibre of the bullet to that of an ordinary rifle, accepting the consequent heftiness of the weapon. Later they added 3 as well. They were also the only nation to emphasise the tactical use of such weapons en masse, instead of distributing one to each platoon or so.
The Swiss, Finns, and Japanese all decided on 2, going to 20mm calibre and producing some prodigiously cumbersome weapons for their poor soldiers to lug about.
The Czechs’ ATR developments were rudely interrupted by the Germans, and so ended up being quite like the Germans’, but with the novelty of the first service weapon to have a bullpup layout.
The Italians, Rumanians and Hungarians all seem to have been content to use other people’s ATRs, either bought from the Swiss or nicked from the Poles.
The French and Americans both sensibly decided that this was a class of weapon not worth pursuing.
The British alone seem to have considered it worth developing a weapon of much the same calibre, muzzle velocity, and overall weight as the original T-Gewehr, whose penetrating performance it exceeded only with the introduction of the Mk II bullet. The belated decision to try methods 1 and 3 from the list above produced a prototype that would have become the Mk III bullet had it been accepted for service, but by that time the PIAT was clearly the way forward.
All the best,