I don't own the 556 Classic, but I've fired them quite a bit. I have to say that they have the best trigger out of the box of ANY assault type rifle I've ever fired.
I do own a 556 pistol...which has not been fired much but I have some plans for it when I can finally get to it (other projects in the way). And I have a 556R on the way. (R is for Russian...it fires the 7.62x39 and takes standard AK mags).
All these SIG rifles are top notch. It's basically a highly refined AK...pull it apart and you can see it's essentially a modernized AK operating system. It is what the AK COULD have been if it had been built by people who wanted to make the platform all it could be.
I'm an AK guy, but the problem with AKs is that quality is all over the place. There are A LOT of them that are crap, there are only a few I would own. And even of those, quality can vary (Arsenals and Saiga for instance).
The VEPR, which is probably the best actual AK you can get, requires a lot of modification from how it comes into the country in order to reach it's full potential. I have two VEPRs, love em both, but it took a lot of effort and expense to get them where they are now.
The Sig has all that goodness right out of the box, for a lot less $$. If you have the opportunity to get one, I suggest doing it. With good optics, a good shooter, and good ammo (Lapua 7.62x39...expensive but worth it if you want accuracy), I've seen this rifle hit out to 600 yards. that's a lot more than should be expected of 762x39, but it's possible.
With 5.56...there are a lot more quality ammo choices. (when you can find it in stock now of course).
SIG did have some quality issues in the past with this series, but the new batches have since been corrected. The current batches have folding stocks. The older, problematic batches have folding stocks that are also adjustable for length of pull...I know some of them were good but quality in the older models was spotty.