Serebii, hands-down. Bulbapedia has 1 or 2 sections that Serebii hasn't, but, not near as much as Serebii's gotten over the years... And the design's better.
Whoa bro, better slow down bro, don't wanna be a bro, bro.
I will say, it's been a while since Serebii has posted a small walkthrough. He only posted walkthroughs for Red, Green, Blue, and Yellow, and once more for Gold, Silver, and Crystal. He hasn't posted a solid walkthrough for the main game since Gen II. IGN is the only place to offer guides, that is, if you really need a guide for Pokemon, which, depending on the part, you occasionally do. Again, Serebii has more info, and features, although I've never even bothered to use the forums/chats.
Serebii: 3 Bulbapedia: 2
Whoa bro, better slow down bro, don't wanna be a bro, bro.
Either really. I find Serebii more appealing due to the changing header image, and the fact that it updates with all the latest Anime and game info, the latter of which there is tons of info on there. Bulbapedia has much of the same, but is in Wiki format, which isn't a bad thing.
They both have their strengths and you aren't really going to be missing out on stuff with whichever site you use.
I use both personally, but I access Serebii much more since the most recent news is clearly seen on the main page.
It's my job to help the next generation, and set a good example for them. And for that I'll gladly lay down my life.
In terms of organization, I find Bulbapedia much more compartmentalized. The way that Serebii categorizes their sections and articles is very confusing; I greatly prefer the cascading wiki style.
In terms of graphical design, I enjoy Bulbapedia's simple contrasts. Serebii's colors, default font sizes, and content spacing are mostly terrible. And I like Bulbapedia's more varied homepage.
In terms of content, they're both great sources of information. Serebii tends to update faster, while Bulbapedia is written slightly better. But they both have unique particular content.
So while my overall inclination is toward Bulbapedia, I also use Serebii from time to time. If you want the ultimate source on all things Pokemon, you'll be using both.