As the above answers state, yes they have the same basic aerodynamic relationships. However what is "about the same" to the experienced pilot can be a world of difference to the new pilot-to-be.

Just a minor change in thrust-line, wing incidence, CG settings, engine power-available, finished weight can each make notable differences.

For example the Great Planes PT-series looks like basically the same as the Hobbico Superstar, yet in flight the PT has far too much dihedral to the point of being, IMO, a "squirrel". The Superstar is a superior trainer, and with power such as the LA-40 it is just a great combination. Now install a Super-Tigre .40 and it is very peppy, yet still in the excellent trainer category.
So many try to put something like the A/f-X 46 in it and it is far too over-powered. The beginner is not yet ready to operate at lower throttle settings plus being able to adjust to a fast (thus more control sensitive) airplane when full throttle has to be applied.

Those that never learn to fly on the wings, but merely the power alone are called "airplane drivers". Those that can and do fly on the wing yet are able to use all the power available are called "pilots". [8D]

So in reality, while airplanes of like-configuration have the same basic characteristics, no two airplanes fly exactly the same for the discerning pilot.