In fifty years and thousands of hours I have found U.S. manufactured light training airplanes to all fly very much the same. But there are certification requirements that have to be met. They basically have to fly like the already approved airplane to be approved. Those standards have been eased with really modern and light sport airplanes. Cub, Campion, Citabra, Taylorcraft, Cessna 120, 140, 150, 170, 172, 180,182,175, Cardinal, Cutlass, 210, Piper Pacer, Tri-Pacer, Colt, Cherokee, Pawnee, Comanche, Twin Comanche, Apache, Aztec, Stinson, Callair A5, A9A, A9B, Gruman Lark, AA1A, AA1B, Tiger, Air Tractor, Stearman, Baby Ace, Mooney, Beachcraft, and several homebuilt airplanes built to these standards, all fly very much the same. At least the controls work the same to the extent there are no surprises.
The Ercoupe, what Wolfgang Langewiesche calls the safety airplane is different. It won't stall, spin, or kill you quickly. It was very unsuccessful here. No macho. It also was a good airplane and easy to control.
I use the same approach in any of these airplanes. I use the apparent brisk walk rate of closure approach. I explain the apparent brisk walk rate of closure approach in "Safe Maneuvering Flight (Low Level) Techniques, which I have posted in this forum.
I use the same takeoff in any of these airplanes. I use the basic low ground effect takeoff, which I also explain in "Safe Maneuvering Flight Techniques.
When I teach new students in simple trainer aircraft, I concentrate on manipulation of the controls to get the exact desired effect. V speeds and Pilot Operating Handbooks (Airplane Manuel) are more applicable to large aircraft (over 12,500 US pounds.) After teaching a new student to fly, I would turn him over to the professional instructors at the airport for preparation for the various flight tests. Our Practical Test Standards for the Private Pilot Flight Test is heavily reliant on numbers found on the various instruments on the panel. Those numbers on those instruments have very little to do with contact flying.