To be picky, both armies also used APCR rounds - which are solid. Interestingly, German (and British) reports comment on how infrequently the bursting charges actually worked - probably more to do with the round shattering on penetration/perforation.
On the OP's question: penetration of materials will take into account such variables as the material being penetrated, thickness, velocity and type of round...
It was almost exclusive to the Western front however, and the reasons were/are rather simple:
1. The average US & British tank was not only more thinly armoured than its' Soviet counterpart, the armour itself was also softer, albeit often more durable, and almost never facehardened.
In other words; In the West, upon impact with the softer armour of US & British tanks, the German fuzes often didn't experience the necessary deceleration force needed in order for them to actuate. In the East the opposite was true, where the harder (yet also more brittle) Soviet armour more frequently provided the necessary initial shock deceleration force for the fuzes to function.
The "flaw", if you can call it that, was that German engineers had designed their fuzes (along with their projectile nose caps) with optimum performance against face hardened armour in mind, which they had expected the Allies to use a lot of. The Allies didn't adopt face hardened armour in any major quantity however, the western Allies instead relying heavily on soft cast steels and the Russians mostly on harder yet more brittle variations of both cast & rolled homogenous armour.
2. The engagement ranges in the west tended to be a lot shorter than in the east, and since the fuzes worked on the simple principles of gravity, the closer the target was, the higher the chance was that the fuze would fail to ignite the bursting charge.
The end result was that whilst the German bursting charges reportedly worked great on the eastern front, a large number of failures to ignite were noted in the west for the larger caliber guns (7.5cm & 8.8cm etc.).
On average however the 7.5cm & 8.8cm BdZ fuzes required atleast a plate thickness of 30mm of RHA angled at 30 deg to actuate at ranges from 500-1,000 m. The further away you were from the target, the higher the chance of a successful post penetration ignition, and vice versa.
The 8.8cm KwK43 was reportedly one of the guns with which the BdZ fuzes hardly ever worked in the west, and when you consider the muzzle velocity of this gun it becomes clear why. The KwK43 fired a 10.4 kg APCBC shell at just over 1,000 m/s, and at 3,000 m it still hadn't slowed down to the 773 m/s muzzle velocity of the older 8.8cm KwK36, despite using the very same fuze.
So whilst the KwK36 would need to hit an armoured target approx. 30mm thick at a range of 500 to 1,000 meters in order for the BdZ fuze to function, the KwK43 would have to engage that same target at a whopping 3.5 to 4 km away to achieve the same! It is therefore little wonder why so many fuzes failed to function in the west, and in the end, as a natural response, a lot of PanzerGranaten delivered to units in the west ended up so without any fuzes screwed into the base.