Some good points made above with regards to the degree to which the winemaker lavishes attention on their GC wines over their wines from lower classifications - though the top winemakers out a lot of care into their more basic wines as well.
In general though, I would say I pretty much ignore the classifications in Burgundy. There are a few GC sites that are a step above all others in the region (RC, Romanee, La Tache, Richebourg, Musigny, Chambertin and Clos de Beze) but there are also equally good PC sites (Cros Parentoux, parts of Suchots, Malconsors, Beaux Monts, Amoureuses, CSJ); there are also some pretty uneven GC (Clos de Vougeot, Charmes (and other) Chambertin - some say Echezeaux, though I think this is generally a very good site, perhaps with some less good producers). In my experience, there are PC sites in Volnay that are superior to parts of Corton GC, and PC sites in Chablis that are equal to, or better, than parts of the GC Chablis vineyards. With regards to village wines, it is rare that you can confuse these with the very best GC but it happens; I had a '66 Gevrey-Chambertin a few weeks ago that I thought was Clos de Beze (of course it might have been declassified GC). It was outstanding - though I would never have guessed; it was an unknown negociant bottling (I can’t remember which off the top of my head). The 1983 Jadot Puligny-Montrachet can hold its own with most White GC Burgundy I’ve had (I’ve had a case of this stupidly good village wine over the last five years - no idea what the story behind it is but it’s amazing).
The morale is, I think, that there is no short-cut for understanding how this all fits together; only in-depth knowledge and a lot of experimentation. And the luck if the draw.