Honestly... both.
Looking back, my PS1 library was slanted towards 3rd party games - Final Fantasy; Metal Gear Solid; Ridge Racer; Tekken. Many of the games were exclusive, but ther ewere a few multi-plats in there too - your Resident Evil's etc.
But surprisingly, a large amount of my PS1 library was Sony published, which at the time I considered first party since they didn't have much of a first party. Actual internally-developed games like Ape Escape or WipEout mixed in with Crash Bandicoot; Spyro; Syphon Filter etc.
This carried on to PS2 - some of the same third parties (Metal Gear Solid; Final Fantasy); some new ones (Timesplitters; SSX) and some of the same first parties (Ape Escape; WipEout) with some new ones (Ratchet & Clank; Jak & Daxter).
Since then, the industry has morphed and I haven't enjoyed the same third party stuff as much. Stuff like MGS and FF still exists and I still buy it, but games like Timsplitters and Ridge Racer have pretty much died out. All the niche third party stuff I loved on PS1 & 2 - Terracon; Gregory Horror Show etc., is long gone. It's rare that a game comes out of nowhere and surprises me like things on PS1 & 2 did.
My tastes are third-party Japanese now (your NIS; XSEED; Atlus games etc.) with a splattering of Sony stuff in there too (I still buy Ratchet; InFAMOUS etc.) And occasionally some European-published third-party stuff like Tropico or Dead Island - don't even ask me why European, but they just seem to still make games that excite me whereas USA largely seems to be still chasing the shootbang crowd.
Anyway, I'm rambling. Both is the answer, I couldn't really pick.