All airplanes fly the same, from a J3 to an A380
I think one might choose a Type a little more modern than the Cub. However, with that caveat, it is not unreasonable to suggest that Types certificated to modern Standards - FAR23/25, for instance, generally will fly in reasonably predictable and similar manner.
That is not to suggest that different Types won't have specific differences, of course.
I suspect that the original statement would have been somewhat along such lines. Certainly, I have heard much the same comment from a variety of competent folk over the years.