Usually yes. Definitely much fresher. There are some cheapy items - onion, garlic - that might be cheaper but the quality lacks. (Better quality also means that you can often use less of a given item if you wish.)
The other thing is that the supers and big box stores don't carry much of a range of items nor much depth. One sees 'black pepper' - and usually that's about it - rather than several from different sources (it makes a difference). And try finding sumac, Aleppo pepper, amchur, lemon thyme, lime juice powder or aji amarillo at a big box store or supermarket.