Why does the broccoli at Chinese take-out restaurants have a crunchier texture than those bought at supermarket and grocery store salad bars?
Raw broccoli is crunchy, and cooking softens it. Usually it's cooked until somewhat softer but still with a bit of crunchiness or at least firmness.  Most likely the very soft broccoli you describe is just more cooked, probably overcooked by a lot of people's standards.

You can't easily tell that much about the quality of the broccoli at that point; the cooking is going to affect the texture and flavor a lot more than anything else. There's certainly nothing here that suggests anything specific about the broccoli (like GMO).

Also, while it's possible that the crunchy broccoli is actually undercooked, many people do like it relatively crunchy. Your soft "crumbly" broccoli sounds much worse to me, so even in terms of the end result, we can't really say anything about quality, just personal preferences. 

I see that you've speculated that the soft, crumbly broccoli is raw. First off, it's extremely easy to tell: the color changes as it's cooked, becoming slightly translucent and shifting to a deeper green, probably slightly less blue and slightly more yellow. Raw broccoli should never be soft, and if it's actually soft and limp then it's very far from fresh. It's also only crumbly in the sense that the teeny darker bits on the top can crumble off. So given that you haven't said it's horrible, it seems more likely that it's (over)cooked and chilled, similar to how you might see chilled roasted peppers or cooked meat in a salad bar.