I can say with 100% confidence and absolutely ZERO doubt that, yes, extract beers can be just as good or even better than all-grain beers.
Now, when it comes to beer quality, assuming you use high-quality, fresh ingredients and you do it skillfully, using good practices, good recipes, and so on, you can make extremely good beers with both. And I personally think it is true that, if you do it right, you will be unable to tell the difference in taste between an extract and all-grain beer. Now, I've never used "old" extract or "low-quality" extract, so I've never tasted the "extract twang" that I always hear people talking about. Nor have I ever made a beer with "just extract" (i.e. no specialty grains, no adjuncts, etc.). My very first beer was a mix of liquid malt extract, dry malt extract, specialty grains, and Belgian candi syrup. I imagine that so-called twang's either a characteristic of stale extract or low-quality extract, but if the stuff is made properly, it really is no different than what you make with all-grain.
Now, that's just talking about flavor.
I think it's similar to the question of "Which is better? Dry yeast or liquid yeast?" Well, most dry yeasts nowadays are of exceptionally high quality and can make amazing beers. As much as I love a lot of liquid yeasts out there, I still use a lot of US-05. HOWEVER, if you want variety, you will want to go with liquid yeasts, because there are so many more varieties and types of liquid yeast than there are of dry yeast, and the only way you're going to get a certain flavor through fermentation is by going with the right yeast, and if that yeast doesn't exist in dry yeast form, then you need to go with liquid.
In other words, all-grain is definitely the way to go if you want the maximum amount of control. You can make creative beers with extract, but you have a lot more freedom with all-grain.
I think Revvy's first post in this thread pretty much says it all.