Fresh garlic contains alliin (two Ls, two Is) and alliinase. Cutting or crushing garlic mixes the two, which starts a chemical reaction that turns them into allicin. Allicin has an incredibly powerful flavor--it's overwhelming, even. Jarred garlic has lots of allicin and there's not really anything you can do to prevent it. To prevent the chemical reaction, you prevent the alliin and alliinase from mixing, and to do that, you keep the garlic whole. I honestly don't think that choosing a different brand or different method of preparation is going to get you any advantages here, this is just how garlic works.

This chemical reaction explains why every method of preparing garlic tastes different. If you use a sharp knife and cut garlic into thin slices, you'll get less allicin and once you cook the garlic, it will be more sweet. The sharp knife doesn't crush as much of the garlic's cell walls. If you crush garlic in a press, the chemical reaction happens at just about maximum speed, and you get a very pungent garlic flavor.

This chemical reaction evolved as a defense mechanism against animals who would eat the garlic bulb. Bulbs in the same family--onions, garlic, shallots, scallions, etc--basically engage in chemical warfare. Humans (and certain other animals) have a number of adaptations which allow use to eat these foods anyway.