In my case, my interest for the Playstation brand grew as the console generations went on.
Back then, the original Playstation was just the way to go because I am and always have been a fan of Final Fantasy and other Square-Enix games. If Square-Soft back then had stayed with Nintendo, history would probably have been very different for me.
But as I bought my console primarily for FF VII and subsequent entries in the series, I got into many other games that made my choice just this much more worthwhile. Games like Metal Gear Solid, Resident Evil, Gran Turismo, Vagrant Story, Twisted Metal 2, Parasite Eve, Final Fantasy Tactics, Bushido Blade, Tobal no. 1, Legend of Mana, Chrono Cross, the Tekken series, Castlevania Symphony of the Night, Crash Bandicoot...
Now, as I mention all these games, one realises that there is hardly any Sony first party games in there (bar Twisted Metal 2 and Gran Turismo). For that generation of gaming, Sony was responsible for securing most of the games I was interested in, hardly for producing them.
I still enjoyed the other 2 systems. But for much fewer games than what was available on the PSX (Zelda and Mario series, Starfox 64, Panzer Dragoon, Virtua Fighter, Guardian Heroes, Sonic...). The PSX library of games I was interested in was expanding at an incredible rate and I had problems keeping up, which can't be said of the other two.
The same exact scenario happened with the PS2. With Sony securing exclusivity for the FF series, as well as Dragon Quest, Metal Gear Solid and many others. Except this time, Sony became a bit more active and produced a few gems that made it on my all time favorites list: Ico, Shadow of the Collossus, and God of War I-II, along with the Gran Turismo series that I already cherished since the original Playstation. I started to think that Sony, despite having produced a game in one of my favorite genre of the time (RPG) that felt sub-par compared to what I was used from the likes of Square-Soft and Enix (Legend of the Dragoon), could wow me in ways only the best developers had done so far. My interest in their first party studios started to rise.
Come the PS3 era. At first, I didn't jump in right away. I judged the system too expensive compared to the competition. Now, I understood the tech that was in there and wasn't complaining about the price. It just wasn't for me at the time since I didn't have an HD TV, and let's be honest here, the first year's worth of games was seriously suffering from anemia. I still needed a console! My PS2 and Gamecube were starting to get fewer and fewer interesting games. Just about everyone in my family had bought a Wii, so I could get into the new motion control craze almost at will. Having always been in love with eye candy stuff (I liek teh Beautiez!!) and since the system had already 2 games I just HAD to play (Lost Odyssey and Mass Effect) I [obviously] went for the 360.
The system hooked me for a full year, made me buy a HDTV, and provided me with some of the best games I've played this gen, namely Fable 2, Mass Effect, Lost Odyssey, Bioshock, PGR4 and GTA IV. But as time went by, I started to take notice of the PS3. Metal Gear Solid 4 was already in my shelf, although I didn't have yet a PS3, and there was Uncharted that looked really intriguing. Final Fantasy XIII was still an exclusive and I wasn't gonna miss it. The 360 was also annoying me with it's pay to play online policy, and I knew the PS3 would let me try the online components from games for no fee. That I wouldn't have to worry of wasting money on something I may not like in the end (I had never been an online gamer at this point in time).
Couple these factors to the fact that I now had a good PC, and that the games that I was looking for on the 360 were also coming out for the PC (Bioshock 2 and Mass Effect 2) or that most other games were ending up being multi-platform and coming out also for the PS3... I started to see less and less value in my 360. I knew there were still gonna be more exclusive games that I would like, but the console would (and did) end up being just like the N64, Saturn and Gamecube from the last generations. Gathering dust in between must own exclusives.
As the generation went on, I started to realize that among all those Multi-platform games, Sony was seriously taking the matter in their own hands. Releasing AAA games after AAA games. The flow of first party games was steady and of a quality that in my book now rivaled those from Nintendo. Games like Uncharted, inFamous, Killzone 2, Little Big Planet, Ratchet and Clank Future, Flower, God of War 3, and the ever coming-one-day-eventually-maybe-perhaps-this-year GT5. When you you add the other exclusives like 3D Dot Game Heroes, Valkyria Chronicles, Metal Gear Solid 4, Heavy Rain and the ones coming like Final Fantasy Versus XIII, Journey and that other Quantic Dreams games (among plenty I forget, I'm sure), you get a steady flow of unique games that keep me occupied like no other consoles I own.
Finally, the PS3 is the console that made me become a fan of Sony as a first party developer. This is the gen that make me say that they now rival the near flawless quality of Nintendo's games. Do I prefer Sony to Nintendo? No. But in my book, they're now equals. I await the next Uncharted and inFamous games just as much as I do the next Zelda, Mario or Metroid. Three of my most beloved series since the original NES!
Tldr version: In a nutshell, while I'm still a huge fan of Nintendo, and Microsoft's Lionheads, Sony is bringing me by themselves more content that interest me than the other two. They also tend to wow me with the so appreciated eye candy more than anyone else on the market right now. So the reason isn't that they're better per-se, just that they cater more to my interests than the others do.
PS: Sorry for the huge wall of text. I just went on and it flowed like that. X_x