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Intelligence. It doesn't feel right to be average or below in intellectual status. You feel you miss out, and luck never goes your way when you're ADD 24/7 (not that that necessarily corresponds to intelligence). Luck, however, is fleeting while having brains is something you can use to your advantage on a routine basis. Besides, you feel lucky when you know more on a subject than someone else.

Depends on the timing.

Sometimes, you absolutely need luck. Say, for instance, the people you were born to. Yes, you were born to your parents, but why those parents? And no, I'm not looking for "Because they did the nasty"! What I mean is, why were YOU, the person, the individual soul, born to EXACTLY those parents? Could you not just as easily have been born to other parents? Perhaps you could have been born to worse parents, perhaps to better ones. And we can imagine that in terms of a successful life, parents are without a doubt a huge factor. Therefore, we must conclude that luck is a must-have.

But there are also going to be times when brains are a necessity. Take landing a job, for instance. Tons of positions are available, all of which can easily be applied to online! It's simple enough to apply to them, and yes, in this day and age luck is certainly needed to actually LAND the position. But to even be considered for the position, you must have the qualifications for the job! And where do the skills that show you're qualified come from? That's right--your brains. Luck plays a part, sure, but brains guarantees you get your foot in the door. Without brains, all the luck in the world won't land you that job.

Plus as Blind said, luck is a fickle thing. Video games will prove this time again--take Fire Emblem, for instance. There are times when my characters will miss on a 95% or so hit chance while my enemies hit (twice in a row) at 30%! Sure, it's not an important example, but it gets the point across. Meanwhile, brains pretty much stay constant (unless eaten by zombies). Using Fire Emblem again, brains tell you how to position your characters (units) in such a way as to give you the best chance to succeed, taking luck out of the equation as much as possible.

So, tl-dr; You really need both.