I have both consoles (and a Wii U in fact) and whilst the PS4 can list more exclusives, the vast majority of them are just really shit indie titles.
The PS4's exclusive lineup is definitely looking up, but until now I feel the Xbox One has had far better exclusives. Things like Dead Rising 3 and Ryse at launch were far more fun than anything Sony had on offer, and since then they've had titles like Halo 5, Quantum Break, Gears of War 4, Sunset Overdrive.
I'm looking forward to The Last Guardian, and I did enjoy games like The Order 1886, not gotten around to Uncharted 4 yet though. LBP3 was just a bit boring, more of the same. I thought Street Fighter V was just fucking awful, Mortal Kombat was way better, as is Killer Instinct on the Xbox One.
But although the PS4 exclusive lineup is definitely improving, so is the Xbox One lineup also. Things like Halo Wars 2 and Crackdown 3 are likely to be box shifters.
All in all I definitely prefer the Xbox One's exclusive list regardless of it's relative size - like the PS4, 90% of the exclusive lists are just utter shit, so factoring out the utter shit closes the gap regardless by shrinking both console's lists drastically.
But really, if exclusives matter at all it begs the question as to why the Wii U isn't the top selling console of this generation, frankly it has far, more, far higher quality, far more fun exclusives than the other two combined - Mario 3D World, Pikmin 3, Captain Toad: Treasure Tracker, Donkey Kong Country: Tropical Freeze, Splatoon, Star Fox Zero, Mario Kart 8, Paper Mario: Color Splash. All these titles are far higher quality, and focus far more on being simply enjoyable than many exclusives on other consoles.
So I don't think you can realistically just relative merits and success by exclusives as an overriding factor anyway otherwise Nintendo would likely win hands down.
I think Sony simply have a powerful brand, and Microsoft ultimately fucked up early on above all else. Nintendo has struggled because it released an underpowered console in the face of last gen, when it should really have waited a few years and released a console with far more competitive specs. Specs shouldn't matter, but ultimately they are used to define or shame a brand, and unless you can pull off an upset as Nintendo did with the Wii where you have a differentiator that genuinely makes the specs irrelevant then low specs will get you fucked.
I think therefore it's really a combination of things that overall define the brand that matters - Sony has a reasonable set of excellent exclusives, it didn't have the DRM/spying rumours of the Xbox One, it has a massive general library, and it was a marginally more powerful device than the Xbox One at a lower price point. Those things combined are what have won things so far for Sony. It's worth noting that the Xbox One has made ground over the last year, I suspect this is because the tarnish of it's own brand from it's pre-release mis-steps are finally fading coupled with the good will it's gaining with new dashboard functionality and support for things like backwards compatibility. One shouldn't forget that last generation we had the exact reverse scenario - Sony started off behind due to a late release coupled with a tarnished brand from the past rootkit fiasco and so on and so forth, but eventually towards the end of the generation pretty much pulled things level with the 360 as the tarnish faded and it regained some good will with some of it's later releases (i.e. The Last of Us).