im basically regurgitating what has already been said lol:
if you want to ride ASAP, and on a budget, get the complete.
if you want something you custom built/tailored to yourself, arn't too worried about money and/or time, and have either the knowledge to build a bike or know someone that can help you out, build it yourself.
i was debating this myself a few months back, and ended up choosing to build myself. i already had a bike, so i wasn't hard up for a bike ASAP.
i also spent way more than i thought i would or would have if i got a complete, HOWEVER over a few months i set some money from each paycheck aside to pay parts....so every 2 weeks the bike grew piece by piece....so the spending wasn't all at once, it was stretched out which wasn't so bad on me economically. Also, since i decided to build the bike myself, i decided when looking at parts to splurge a bit more and get really nice components at times, where if i had bought the bike all at once would have settled for less. In the end, the bike came out to be better (in my opinion) than anything i could buy stock for the price.
Also, another thing.... i knew VERY LITTLE about bikes in general before deciding to build. However, needing to buy components forced me to learn about each component, so I sort of thought of the additional cost of building the bike instead of getting the complete as going towards bike education. Stuff i didn't know about, like say, installing a headset or crankset, i needed to learn about before going ahead, so i consulted the internet, my brother (ex-bike mechanic), and my local LBS.
so in the end, i got a really cool (at least in my eyes lol) bike and learned a ton in exchange for time and money. a trade off i think is worth it.