Is fresh healthier
Garlic is an incredible superfood, no matter how you eat it. Some people find that raw garlic is difficult to digest in which case pickled garlic might be a good choice. It's a bit of a trick question because I don't know how it has been pickled--are we talking commercial chemical laden pickling? lacto-fermented? home-style organic? These things do matter, adding commercial chemical preservatives destroys nutritive value (in my opinion). Old style pickling/fermentation can actually add nutritive value and make something like raw garlic much more digestable. (Tried black garlic yet??? YUM!)
I agree with Slow Cooked. The fermentation process can actually add to the health benefits, provided it is fermented without preservatives. There is a book called "Wild Fermentation" that I highly recommend that explains the benefits of fermentation and detailed instructions on how to start fermenting at home.