The way the nsx feels to me mimics its shape, as a wedge the weight is so apparent right behind you. it initiates turn in so well, and the mass behind you seems to help the car rotate into corners. Up to 7/10ths this is a huge advantage and makes it feel like its on rails, and that you're in total control of the car. But when you exceed that limit, or get near it, it becomes an experts level driving car very quickly. I haven't driven the gt4, but I spent a few days with the cayman R. While they're both mid engine cars, I wouldn't say they felt similar at all. The cayman is just so easy to drive fast, its suspension feels like its filled with the most expensive rubber. That being said, ill take the NSX 10 times out of 10. The feedback is like a seeing a band in person at a small venue with great sound, vs hearing the cd from another room.
It appears to me from the 1st video, you are braking later than the cayman coming into corners. At around 1;40 you can see this as you begin to gain some ground in the turn but then have to lift to correct, meanwhile he's taken the "slow in fast out" approach, and begins to pull away. its possible working on your style to better match the cars strengths could gain you that pace you're after.
Please take my comment as it was intended, to help, not to criticize your driving. I admire anyone who takes their NSX to the racetrack.