The 562xp weighs 2lbs less than the 372 according to Husqvarna's website, and is also significantly smaller in size.
When I cut firewood, I cut typically from sun up to sun down. The 562 weighs 0.2lbs more than my 455 Rancher did, but has 1.2 more horsepower (35%), revs at higher RPM, and does not need carb adjustment. Auto Tune is an awesome thing.
The 372 is too big of a saw for me to use for 14 hours straight. The 562 is perfect. I've found that the Rancher, or home owner saws in general, are not particularly fond of plunge cutting if you need to do it. I accidentally plunge cut a few times while undercutting with the 562 and didn't even realize I was. If you do a 60cc saw comparison side by side with every other chainsaw on the market today, you will not find one with even close to the same horsepower that the 562 has. I tried. The Auto-Tune is what does it; and I learned that CC's don't mean much at all, it's all in the horsepower ratings. I really didn't want to end up becoming obsessed with a $650 saw that was way above my price range, but I did, and there isn't any alternative. I now must have one, and once my taxes come in, I'll be getting myself a brand new one.