My experience has been the hardnecked has bigger cloves.
You’re right - the Hardneck varieties tend to have fewer but larger cloves.
On years when I grow it, I grow Northern White and/or German Porcelain. Of course, I’ve been known to plant the random garlic bulb that fell on the floor at work and couldn’t be identified, too. Waste not, want not! ;)
They’re sold out now, but here are the Garlic varieties from Jung’s:
https://www.jungseed.com/category/s?keyword=garlic