I suspect, without proof but read next paragraphs for some evidence, that the US offer their surveillance net. If EU police is searching for someone, even in our own territory, it's easier for US intelligence agencies to locate and eavesdrop on the suspect with the tech that we know.
El Pollo Carvajal [0] was arrested in Madrid, September 2021. Although it was our police that made the arrest, it was the US that provided his exact location. Some say that local authorities had no desire to catch the man, actually he had already been arrested in 2019 and "disappeared" apparently due to some bureaucratic error. If I'm not mistaken, he's awaiting extradition.
The end of terrorist band ETA [1] (that Wikipedia charmingly defines as "separatist group") happened after a continuous string of high-profile arrests in France. Again, our neighbours haven't been always very collaborative, but had no option when alerted of exact location of people in the Interpol watchlist.