Both planes have the same wings, the same control surfaces and cockpit controls, same fuselage, same engine. You can "feel" all the difference you want. Doesn't change the facts.
If I were a betting man I'd bet the only real difference is that you know you're in an La-7 or an La-5 and your own preconceptions are the cause of your feeling.
So you are taking all human intuition out of the flying of the planes and basing everything on their statistics? I can see why you haven't played in so many years. Must be a very boring game for you. Still, there is SOME statistical difference between the two planes, you have admitted this much yourself. I, personally, can feel it when flying them.
I don't feel any significant difference between those two in handling, satbility and so on. As far as I am cocnerned, they virtually fly and fight the same to be, only notable differences are high speed acceleration and top speed
Do you ever fly them at under 100mph for hours at a time in the DA practicing rolling and vertical stall fights 1v1?
Do you ever deliberately fly to the edge of the envelope in any plane?
I am almost certain neither of you two have ever displayed any innovation or style to me in a dogfight and therefore I doubt you will ever understand how a player can feel the subtle differences between two such similar planes.