roasted garlic vs. raw

As covered on wikipedia, raw garlic has a number of sulfur-containing compounds, among them allicin, which are responsible for the burning feeling raw garlic imparts to a dish. When cooked into food, these flavors mellow and the compounds are boiled off or denatured. Other enzymatic and non-enzymatic transformative and browning processes also take place as garlic is cooked.

Roasting garlic produces these changes in garlic before-hand, and in a more controlled way. As the garlic heats up and starts browning, the raw garlic character is lost, while sweetness from melanoidin (a product of the reaction of amino acids with sugar, per the Maillard reaction) and savoryness (from the denaturing, concentrating amino acid content) are gained. The extreme example of this is Black Garlic (discussed at some length on my blog), in which the sweet and savory content of the garlic has been processed and concentrated over the course of a month, with the flavor resembling non-sour Balsamic vinegar.

With that said, the inclusion of raw or pre-processed garlic will depend on the proportions of the two above-noted sets of flavors that are desired in a dish. If added raw to uncooked food, it will add very little savory or sweet, and plenty of aroma and burn. If added roasted to that same food, it will add mostly savory and sweet, with very little of the burn. Any further cooking that takes place after garlic's addition to a recipe will further discourage the raw flavors and aromas.

It's actually pretty simple: as you put it, roasted garlic is milder and sweeter. So if you're looking for a sweeter, milder garlic taste, you'll want to use roasted garlic. Applications such as 40 Clove Chicken, where garlic is the primary flavoring agent, tend to use cooked whole cloves to avoid overpowering the dish with sharp tastes. (Whole cloves are also less strong than smaller pieces of cloves, in general).

Onion is much the same way; if you want a sharp bite to your dish, you'll keep the onions as uncooked as possible, whereas a more subtle flavor can be had from cooked onions. For a good example, try a burger with chopped but raw onions as opposed to a burger with sauteed onions.

Basically, you pick the cooking method of the garlic based on what flavor profile you want the dish to have.

I would think that science has little to do with it but rather more a matter of texture and aroma. Raw garlic is much more aromatic and "spicy" since it's natural aromatic compounds have not been altered by heat and it is also much more firm obviously since the cell walls are still generally intact and rigid. I find that approaching garlic is a lot like painting a wall, do you want it to shine through, accent, or blend in? Depending on how you answer that question it can range from raw, sauteed, roasted, fried, sliced thin, pureed, etc. But scientifically, I don't think that outside of shared aromatic compounds with certain foods the way it is used makes a difference.

You can also go to https://www.foodpairing.com/ and see how different foods pair together based upon shared flavor and aromatic compounds found in each.

Science? No Logic? Yes -what sort of flavor do I want/need? does it go? how much?. I play with garlic many different ways (shaved, chopped, minced and whole) and it does seem to find its way into most of my dinners. Rarely, however, do I roast it. If I do, it is usually for a stew, an herbed butter, or some sort of cheese board or orderves.