I'm actually surprised no one has yet brought up the Japanese using "Bamboo Bullets"
There's no end to the inventiveness of the rumor mill, and sadly, sometimes belief in those BS stories causes actual harm.
In the Pacific, at Guadalcanal and places like that, troops were given Atabrine to combat getting Malaria. But many troops didn't take the meds, because of a persistent and utterly baseless rumor that the medicine would inhibit sexual performance. Some of those guys got malaria, and some probably died from it.
Was the Other Guy's stuff always better?
Regarding WWII small arms, I'd say, "No, not
always, and actually, not often."
A very few of the enemy's small arms were a bit better in some ways than some of ours, and there were some they used we had no counterpart for, just as some of what we used they lacked a counterpart of their own.
Sticking with service class guns, lets look at who used what (generally)
Pistols:
The US used the .45acp 1911A1 and (mostly S&W) .38 special DA revolvers. The .38s were mostly used by aircrew, but not exclusively.
Germany used the P.08 Luger, the P.38, as primary but also used the FN Browning Hi Power, all in 9mm Parabelum.
Italy used the 9mm Glisenti, which used a round dimensionally the same as the 9mm Luger but lower powered.
Japan used various models of the Nambu semi auto in 8mm Nambu.
All the nations also used small numbers of other pistols including revolvers.
(interesting tidbit, Japanese officers could buy their own pistols and use them, and quite a few did. One local vet I know of really wanted a Nambu as a trophy. He finally got one, the 4th pistol he captured. The others were S&W .32s or .38s in well made Japanese style holsters)
RIFLES:
US, the M1903 Springfield, the M1 Garand and the M1 carbine were the main ones. .30-06 and .30 carbine.
Germany's mainstay was the 8mm Mauser Kar 98k though other types also saw service. Germany had no direct counterpart to the US Garand or Carbine until 43 and the semi auto rifles they developed then never came close to replacing the Mauser 98.
Germany did develop and field the assault rifle in small numbers in 43 and much greater numbers in 44-45 but again, not enough to become the general issue rifle. The US had no direct counterpart to them.
Japan used the Arisaka bolt action in 7.7mm Arisaka, alongside the earlier model in 6.5mm Arisaka.
Italy used the Carcano in their 6.5mm caliber and later added the 7.35mm Terni. both bolt actions.
None of the Axis powers had a counterpart to the US BAR, though Germany did make the FG 42 for their paratroops it was never in widespread use like our BAR.
we'll leave SMGs and machine guns for next time