Phantom Zone is much bigger than Dark Dimension.

Mainly because the Phantom Zone has better evidence proving its size while Dark Dimension is uncertain in size due to lack of evidence, most of the time it is speculation.

The Phantom Zone is a realm of The Sphere Of The Gods, in fact it is the underworld itself or also known as void.

Basically the Phantom Zone is the limitless void of the underworld, the same void where ALL the Universes were born and where they will all end.

Which means that the Phantom Zone is a dimension large enough to cover all the space where the entire Multiverse was born.

More recently the Phantom Zone was shown to act as a permeable membrane (barrier) between the main Multiverse and the Dark Multiverse.

That means that the Phantom Zone is a barrier between both layers of the Multiverse, basically the Phantom Zone covers every reality of the main Multiverse and covers every reality of the dark multiverse, enveloping the entire DC Multiverse.

And if the conclusion of Death Metal weren't enough now the DC Multiverse is bigger than EVER. since it became a kind of Omniverse with infinite Multiverses within it.

Which means that the Phantom Zone is also larger than EVER as it encompasses an entire Omniverse with infinite Multiverses within. more so now all the ages that DC has had are now an age because everything has been fused so now it's just one story.

The Phantom Zone is BIGGER.