How does the way that I cut my garlic affect the taste of my food?

@Adam A is close -- it's not an issue of surface area on potency, it's an issue of damage to the garlic. The 'strong' taste of garlic comes from a reaction as chemicals are released so they can mix (alliin and alliinase)

When you cook the garlic whole (as you would for roasted garlic), you will never get this reaction, as you'll break down the chemicals. Also, the chemicals break down over long cooking, so even if you add a head of crushed garlic at the beginning of a batch of slow-cooked tomato sauce (4+ hrs), it's not going to have as strong a garlic flavor as adding a clove or two at the end.

One other way that the garlic prep can affect the taste is when you're sauteing, stir frying or other cooking over high heat -- larger bits can be cooked longer before they burn ... and burned garlic is bitter, acrid and will ruin any dish. (if you burn garlic, stop immediately, trash everything, clean the pan, and start again -- there is no way to save it that I know)

More surface area means more taste. The more cuts, the more potent the garlic flavor will be.

It also affects texture and homogeneity - if you're coarsely chopping the garlic, you're going to feel it when you bite into it. You also are more likely to get some variety on each bite (which I think can make a dish more interesting).

@Joe said most of the thing I could, but maybe let me add some more information in terms of cold marinades and eh, perhaps, sous-vide cooking.

Cold marinades - Larger garlic coarsely chopped, provided that it is not cooked, allow for a fresh release of garlic flavor on chewing, this may be a desired or undesired effect. Otherwise one can consider Fine, minced garlic paste for the job, which is usually easier to control.

Sous-Vide cooking - if you do it, you should be able to know, but just in case, use very small amount of garlic paste or powder if you plan to use garlic, anything more than a slight pinch would result in disaster. I learnt it the hard way.

I've found that recipes that call for coarsely chopped garlic fully intend for you to get a mouthful of garlic to chew down on -- where garlic is a "star player" in the dish, whereas a recipe that calls for a bit of minced garlic is usually looking for garlic to play a more "supporting role" in the dish. There are, of course, exceptions to this, but I'd be willing to bet that 9 times out of 10 this would be the case.

Not exactly as scientific as @Joe's response, but it's an alternative way of thinking about the big pieces of garlic in a dish. They might not flavor the whole pot as much, but if you get that one bite with the whole clove, you're definitely going to taste it!