Question: I am going to buy my first proper road bike, and I have been comparing entry-level carbon frames with top-level aluminum frames in the same series (Giant Defy). What are the benefits of carbon vs. aluminum frames? Is it better to get an aluminum bike with higher-end components or a similarly priced carbon bike with lower-end components?

Answer: 
Essentially this is about low end carbon versus high end alloy. Carbon is typically lighter and less harsh (more vibration absorption) than alloy, but is not as robust. I doubt that the alloy is much heavier. I think it will come down to the difference in component quality and your budget.

Personally for a training bike I would probably go for the alloy, but that is driven by my financial situation. If the bikes are of similar price and the components are of the same quality, I would consider the carbon. However I would not trade component quality for a carbon frame.

Edit : Seven years after the answer was give.
Many of the techniques learn laying up carbon, and with advances in hydroforming alloy, have lead to allow alloy frames that are significantly cheaper to fabricate yet nearly as light (if not lighter) than low end carbon frames, while having the characteristics of stiffness and compliance where wanted. You can no longer discuss 'Carbon' and 'Non-Carbon' frames as most major manufacturers have 2, 3 or more variations of carbon from 'cheap and cheerful' to 'insanely light and expensive'. The cost saving in Alloy frames put into better components leads to a better bike for the same build cost. As carbon is considered more desirable by many, it fetches a higher price for the bike.

TL;DR when buying a bike, look at the whole bike, not just the frame.
If I were you I would satisfy myself as to the quality of the carbon frame of the bike you're considering, and provided it looks decent, to go down the carbon route.

The reason for this is just upgradeability. It is conceivable that as you become better and stronger on your first road bike, sooner or later you may find yourself asking the question "how can I make my bike faster?". 

Now, for most of us the answer to this is to lose 10% in weight and 10% in body fat, but that's a different story ;-)

But when you start to think about upgrading parts, you've got your groupset, wheels etc. These things you can generally upgrade at your own pace, and as your budget allows. And they would apply to any bike, carbon or not.

I think if you have a non-carbon-framed bike, however, one of the big things to think about as regards an upgrade is the frame itself, i.e. basically buying yourself a new bike. And, of course, this will be pretty expensive and not really something you can do piecemeal.

In summary I would probably go for as good a frame as I could afford, and initially sacrifice things like groupset, just on the grounds that I can upgrade this kind of thing later as and when funds allow.

Incidentally I have a Giant TCR Advanced and think it is superb. I have no experience of the Defy but if the workmanship is like the TCR I doubt you'd be disappointed.

One last thing, since you say you're based in London and especially if cost is an issue....you could do a lot worse than looking at the Chris Boardman range out of Halfords. Just look at the awards these bikes win, you really do get a lot of bang for your buck.