Of the two I have only been to Beauval, and that was before the Dome and the South American Aviary opened. Köln looks excellent as well, but I am slightly leaning towards the French collection here. And that isn't because of species numbers (I agree that when both collections are so large, one zoo being ahead is barely notable), just that I really love everything that Beauval has on offer in this category.
The lemur and colobus islands near the entrance are gorgeous, offer tremendous height with mature trees, and are the perfect introduction to the zoo. The row of enclosures in Monkey Pathways (when I visited, they had the far better name of 'Primates Peculiarities') are really charming - rows of sizable, enriching cages for really interesting monkey taxa, including Moustached Guenons, backdropped by the gorgeous woodland that covers the central half of the zoo. I also really liked all the ape enclosures, in particular the green and lively chimpanzee island, although in hindsight the orangutan one is quite limited in terms of climbing. All of the other enclosures throughout the zoo were really nicely done, too. The two langur cages near the pandas struck me as very spacious and well-designed, again with the surrounding nature enhancing the scenery, and I love the huge, grassy lawns for more terrestrial species like Barbary and Lion-tailed Macaques. Since my visit, things seem to have only gotten better with the arrival of doucs in the Dome whose enclosure looks rather nice.
It has been mentioned upthread that Beauval's enclosures lack vertical height and climbing. Perhaps I am underestimating how much height is needed, but it seems to me that other than the orangutans and perhaps the howlers in the new aviary (but even then it looks sufficient, difficult to get a sense from photos) all the primates at Beauval are very well-catered for in their climbing needs. Would be interested to hear more about this. Unless I am missing something, then I would echo what
@pipaluk said in Beauval's previous thread about how people tend to assume that Beauval's enclosures all have some sort of deeper issues below surface level just because a few of them do. To reiterate, I don't want to sound hostile here, and would be happy if proven wrong. Either way I feel as though whatever these issues are, with the caveat that I haven't been to Köln myself, they cannot be worse than the almost complete lack of climbing and space in those outdoor cages of Köln's Madagascan house or the overstocking of their baboon island...
All that said, this really is a phenomenally close tie. Looking at photos, several of Köln's offerings look really impressive, in particular the South American House. I hadn't heard of that exhibit prior to this thread, and it has certainly climbed up my zoo exhibit bucket list! A historic, architectural marvel with a modern interior, balancing animal and guest needs. Definitely shouldn't be more than a 3-2 in either direction, I think.