They both have their pros and cons.
Overall, I do prefer Xbox Live, but not by much since they are kind of different. The interface is a lot better to use, the gamertag system and user rating is also good, and there are a few more functions to it, plus it's a lot more "useable" in the middle of a game.
Sony's biggest mistake with the PS3 was to not include a free headset. This completely ruined online play compared to Xbox, because everyone was constantly chatting and meeting new players on Live whilst everyone on PS3 was and is a lot more quieter. Live is a lot more social, overall, because it included a free headset.
The good thing about PSN is that it's free, and there is a lot less advertisement. It's more about the console and games, and less about trying to sell you stuff and shoving all this online content in your face like Microsoft do. I'm very disappointed that PS4's PSN will have a paid subscription now, and I have a feeling they'll go for an Xbox Live approach with more advertising and more content promoting.