Even if a blue beats a purple, a purple understands more. They feel the roll instead of planning the roll. A purple can take advantage of mistakes because they feel when something is not right. Their defense is better because they beat you to the position (ex: instead of you breaking their guard, they release their guard). Their basics are better (elbows in, never be flat, etc). They rarely panic and are comfortable with being uncomfortable.
You may have a series of moves that allow you to get into a dominant position and dominate them (“beating” them) but they still understand more about the sequence.
Offensively, they can link moves, read what you are doing and set up their finish. If they try a cross choke, there is probably something else they are going for. Purple belt is about fooling a blue belt to fall into a defensive trap to give up the intended submission. If that fails, a good purple has a third or fourth option.
So many people quit at blue. A purple belt has been around the block. They are good at what they need to be good at, but are willing to try new stuff against the right guys. They are usually hard to submit because they are getting beat up by browns/blacks that are much more strategic than they are.
Blue is usually an ego belt (initially). Purple is not an ego belt but more of a learning belt. Once there, the grappler comes back to reality and realizes how little they know.