I've had both since their respective launches and I've always preferred the PlayStation 3 for various reasons.
XMB - It's well-organized and I like the minimalistic approach compared to the 360's slightly more graphic-heavy interface, especially after avatars were introduced.
Blu-ray - I buy all of my movies/shows on the format whenever possible, really nice to have.
DualShock - It might sound odd (I don't really understand it myself), but I don't like the "comfortable" shape to the 360 controller. PlayStation, NES and SNES controllers are among my favorites.
Region free - Not something I use often, but it's nice knowing it's there. I import certain 360 exclusives, but not as many as I'd like since the majority of them are region locked. I also like being able to hop onto the Japanese PSN and grab the occasional demo for a game we've yet to get.
Free online - Not that I acually play games online, but besides the occasional PSN Plus early access, I get demos the same time everyone else does. No premium period like Silver users have on XBL. Also, because I have a Netflix subscription, I can access that for free, just like every other device under the sun (besides 360).
As for games, they're pretty close. Thanks to their desperate attempts to break into the Japanese market, Microsoft bankrolled Mistwalker and we got Blue Dragon and Lost Odyssey out of the deal. I imagine they also pulled a few strings for Tales of Vesperia. Three of this generation's best JRPGs. Not to mention Cave, Treasure and a number of other shmup developers have set their sights on the 360. On the other hand, PS3 boasts the likes of Valkyria Chronicles, Metal Gear Solid 4, Yakuza, etc. Looking forward the PS3 has more that's caught my eye, like Final Fantasy Versus XIII (for now) and The Last Guardian.
I do like XBLA though. Probably the best thing to ever happen to the 360.
They're both fairly disappointing to be honest. PS3, 360 and Wii combined still manage fall far short of the PlayStation 2 alone.