I would say that the limiting factor on faster lap times is more confidence on the bike, considering they are very similar.
The difference in the bikes is not linear. It is not that you go faster (speed) on the newer bike because it has more HP ( although it does) and it is lighter (yes it is).
It could be the balance of the bike, the balance/power delivery of the engine, the way the electronics makes sure that the bike puts the rubber where the road is.
The extras that the 15R have vs. the 13/14R is what can give you confidence to go faster.
I fully agree that confidence is the biggest thing when it comes to going faster (until somebody is running at the pointy end of the Expert grids, when equipment/setup actually has a tangible effect). I have often said you could take the bike from somebody running track days, then bring it back in an hour (having not done a damn thing) and tell them the suspension has been "expertly setup", the brakes have been flushed and bled, and the tires have been rebalanced and are pressured optimally for the conditions......and that person would go out and immediately go faster....even though nothing has been done to the bike.
Confidence is the primary thing holding back most people. The vast majority of riders aren't riding anywhere near the max capabilities of a 2003 R6, much less a 2013 1199R.
My point is that instead of taking an $8000 hit by swapping a 13R for a 15R, somebody could easily just take the 2013 to Dave Moss or Thermosman (Mike Fitzgerald) and have it properly setup, then change some things like rearsets/levers/clip-ons to make the bike more comfortable, then put on some better tires and boom....more confidence. Which means faster lap times.
I still hold to my original point, if somebody is running 1:30's on a 13/14R, they will run 1:30's on a 15R. Sure, there are differences in the bikes, but unless somebody was riding a 13R to its max potential, any differences between the bikes are theoretical (meaning unrealized potential).
In other words, if somebody drives a Camaro to work every day and they decide to trade in their 2010 Camaro on a 2015 Camaro because the 2015 is "faster" or "better"...but all they do is drive to work every day...then any performance difference is unrealized. If somebody never gets over 60mph going to work, then what difference does it make if the newer car is faster (on the spec sheets or because it has better parts)? The specs might be better, but they wont be any faster personally because they werent driving the 2010 Camaro as fast as it could be driven.
If what is needed is more confidence, there are ways to get that without changing bikes.