The PlayStation 2 titles recently introduced to PlayStation 4 perform differently in Europe than in North America.
Digital Foundry noticed that the European releases of PS2 games running through emulation on PlayStation 4 suffer from frequent stuttering that is not seen in the North American releases of the same games.
The difference stems from the game versions being emulated in each region. While modern TVs support 60 FPS refresh rate and higher, PlayStation 2 games used to run on analog TVs that were locked to 30 FPS in North America (NTSC) and 25 FPS in Europe (PAL).
In order to be consistent with today's standards, Sony decided to boost the European versions of emulated PS2 games to 30 FPS through frame blending. This should work fine in theory, but in practice it caused the games to stutter frequently as shown in Digital Foundry's video below.
Given that there are no technical differences between European and North American TV hardware, we recommend using the North American PSN storefront to download emulated PS2 games.