I'm a fan of hardneck garlic strains -- i've only experienced strains from the rocambole and continental types of hardneck garlics, but none of the Asian types. I don't think i've ever seen one.
Hardneck garlics feature a stout-stemmed flower stalk, which, after harvest, leaves a hard and inflexible "neck" or trimmed stalk on the bulb.
Three favorite strains:
1) Spanish Roja The word "roja" is Spanish for the color red. A Rocambole garlic with a flower stalk of about 4 feet (1.3 meters). Flavor is extremely sweet, very garlicky, but it can be used raw with little of the stinging bitter taste found in many garlics. Cook lightly... overcooking can kill the flavor, or at least diminishes it.
Disadvantage: It only stores for about 3-4 months.
2) Persian Star Grows to about 6 feet tall. A Continental Purple garlic. Flavor is quite sweet, when raw is a bit 'hotter' or tongue-stinging than the Spanish Roja.
3) Georgian Fire Can reach 7 feet in height. Very hot, and, unlike hot peppers, this strain is one i find quite unpleasant if consumed raw. However, it is the finest garlic for roasting, retains all of its garlicky goodness and has the richest flavor of any roasted garlic i've tried.
Note that all these varieties have larger bulbs than the more-common softneck garlic strains that you usually purchase in your grocery store, with fewer (much larger) cloves, and are much easier to peel. This late, you may not get full-sized bulbs, but you'll notice a big difference in flavor.