For me it comes down to a big trade off: the emotional highs of continuity, or the fandom and community energy that peaks during a show's actual airing months. Anime is basically the only TV I watch (though my wife and I have Netflix, and I'll occasionally watch something with her), and so I have a lot of fun agonizing about episodes throughout the week (an experience I don't get with any other shows or medium). That said, if I have a choice, I nearly-always prefer to get an entire season at once and watch it in bulk sessions.
I think I prefer it that way because the shows I watch are character-centric, not action- or otherwise, and so having week-long breaks can break up the periods of character-watcher bonding that happens .
To offset the negatives, though, I try and participate in online show fandom during the week. For me, that's a big part of the fun: experiencing the community of a show during the original airing. There are some fun and passionate people out there, and it's a blast to participate.