I've run a session with a moon druid, and several friends of mine have as well. The overall consensus in my little gaming community is that the moon druid is absurdly OP at low levels. With healing at a premium in 5e, any way to get free hp is automatically very helpful. When that way of getting free hp is accessible twice per short rest and comes along with an attack that outdamages the fighter, it's just overkill. AC simply isn't relevant: since it's free hp, even if it set your AC to zero, it would still be really good. Not to mention that you also have a nice selection of cool spells. The wild shape and the spells combo together nicely, because you can cast spells more aggressively knowing that you can always fall back on wild shape if you run out, and you can wild shape more aggressively knowing you have spells to cast if you run out of wild shape.
The guidelines in the DMG recommend about two short rests per full adventuring day. Those rests aren't mandatory, of course, but classes like the warlock seem to be assuming they'll get those rests more often than not. But if you do that with the moon druid, they're getting six wild shapes per day, which seems extreme.
At level 5 or so, it seems to even out and become more reasonable, although still very strong, but around levels two and three it's way overpowered. I guess if you just don't care about balance at those levels, it's not a big deal, but I often run shorter campaigns that only cover a few levels anyway. In that style, a moon druid could be ridiculous for a significant majority of its time at the table.