Most importantly, you have to recognise that OSF doesn’t face anywhere near the same size and weight constraints as PIRATE. According to the brochure for PIRATE, the unit has a volume of less than 10 litres, and a weight of 8kg (though I would think it’s heavier, but oh well). For comparison, the constraints for OSF were 88 litres and 100kg, so a lot more functionality can be included.
The sizeable difference is likely due to space being reserved on the Rafale for the future OSF as early as 1988 in the design phase. This is probably not the case for Eurofighter.
In terms of functionality, PIRATE is for the most part a dual field of view thermal camera for very, very long range applications:
Spoiler
The narrow FOV is used for target search and tracking (~8° x 11.25°). The wide FOV is used for identifying planes. It also only operates in a single waveband (LWIR) which is disadvantageous for air-to-air applications. MWIR is preferable due to its greater sensitive. Having both is best.
On the other other hand for OSF, due to the less severe size and weight constraints, the thermal imaging channel (used to detect targets) can operate in two wavebands (MWIR and LWIR) which enables better target discrimination and performance in different weather conditions.
Spoiler
Due to more efficient target discrimination, the thermal imaging channel is able to afford a larger field of view for situational awareness (~80° x 60°) at the expense of resolution. This cost cannot be incurred for PIRATE since the single thermal camera is required to have a very high resolution for target identification and efficient clutter rejection.
Identification by OSF is instead performed by a separate sensor, the CCD visible detector. This is essentially a long range telescope with a FOV of less than 1°. It therefore has a very high resolution for target tracking, and can determine the range via a 300mJ laser rangefinder.
Both the thermal imaging and visible sensor are also on gimbals (unlike PIRATE) which provide a far greater field of search:
Spoiler
TL;DR: OSF can afford more functionality and performance due to being heavier and having over 9 times the volume of PIRATE. PIRATE has to make significant compromises to meet constraints, OSF not nearly as much.
/rant over