Freeze or refrigerate bread?

Methods, from best to worst (assuming the bread is in a sealed plastic bag):

1. Freezing
2. Room temperature
3. Refrigerating

According to the FAQs for Dave's Killer Bread, which does not use preservatives:

Q: How should I store my bread?

A: The best way to store your bread is on your counter or in a bread box at room temperature. Take care to keep your bread away from sunlight, heat, and high moisture levels, they can cause the bread to mold early. Yuck! To store bread for extended amounts of time (up to three months), put a second bag around the original bag, seal it tightly, and place it in your freezer. Thaw slices as you need them. Storing bread in the refrigerator will keep your loaf from molding; however it may also dry out your bread. We recommend freezing bread if you can't possibly eat it all, but good luck with that.

Refrigerating doesn't slow down the starch recrystalization process that causes bread to stale. According to "Does Refrigeration Really Ruin Bread?":

When bread is stored in a cold (but above freezing) environment, this recrystallization, and therefore staling, happens much faster than at warmer temperatures. Freezing, however, dramatically slows the process down.

Presumably moisture is lost during the starch recrystalization process.

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Actually, moisture retention or loss has very little to do with bread staling:
Simon Field, Culinary Reactions, ch. 11 "Heating":

Heating starches changes crystallized starch molecules into gels. Bread becomes stale when the starches crystallize, and warming the bread returns them to their soft gel state, making the bread taste and feel fresh. Stale bread is not dry; it just feels that way because of the crystallized starches. In raw potatoes, the starch is compact, but heating makes the starch granules swell and absorb water, becoming soft and easier to digest.