shredder111,
As an instructor let me jump in here and tell you what the difference is. The big difference between trainers and the planes you are talking about is that the trainer is designed to fly slower, be very stable, more rugged, and have self righting capabilities.

Flying slower. When you are learning to fly the speed of the plane makes a huge difference, the slower a plane flies the longer you will have to think about and prepare to do something. For instance, if I tell my student to fly a pattern I will tell them to fly a rectangle and make turns at certain points. With a fast flying plane you may have 2-3 seconds before you get to a turn, but with the trainer you could have 5-10 seconds. 3-8 less seconds may not sound like a lot to somebody who hasn't flown, but when you are on the controls it can seem like an eternity. I still fly my trainer even after almost 10 years of flying and I like to make a little joke. When you are training your trainer will seem like it's flying SO FAST, but after you learn and you fly the trainer you wonder how a plane can FLY SO SLOW!!!!

Stability. With the intermediate planes you talk about most of them are low or middle wing planes while trainers are always high wing planes. There is a simple reason why they are like this. With a low wing plane the mass of the plane is balance above the object holding the plane in the air (the wing), natural forces want to tip that weight over this making the plane a little less stable. But with a trainer being a high wing the mass of the plane is hanging below the wing, this makes it easier and more stable.

More rugged. Good trainers are designed to take a little extra "abuse" that happens when you are learning.

Self righting. Most more advanced planes like you are referring to are more maneuverable because they go where you point them. The dihedral and high wing design of a trainer makes it self righting. If you use the aileron and make a turn you can release the stick the dihedral will cause the wing to come back to level flight. More advanced planes will require you to bring the wing back to level flight by applying left aileron.

And lastly, frustration. Both yours and the instructors. With a more advanced plane the instructor is going to be "taking over" the plane more often he might with a trainer. Trust me, after a little bit of this you as the student are going to get frustrated by this because you "think" you can handle it. The same for the instructor, he is going to have to constantly keep taking control of the plane. While it may not seem like it to you, it takes a lot of concentration on the part of the instructor when he has a student on the buddy box. When I am teaching a student I will "fly" the sticks right along with the student, meaning I will move the sticks reacting to what the plane is doing. By doing this I always "know" exactly what to do to save the plane if I have to take control of it. By getting a faster more maneuverable plane you are going to increase the work and stress load on the instructor. In addition to that, it's probably going to take you a lot longer to learn to fly on a more advanced plane than it would on the trainer.

Now as an instructor I simply won't teach people that show up with planes other than a trainer. Why? Several reasons. First of all they are harder to train than most. How do I know that? Well, first of all they think they know better than everybody else and don't need a trainer to learn. This shows me that they aren't going to listen to what I tell them when they are in the air. Next is the stress and work load on the instructor. Like I said above, it takes a lot of effort on my part to teach somebody. Why in the world would I want to increase the workload and stress on myself just because a student "thinks" he knows more than everybody else?

I know that this may have sounded a bit harsh and I'm sorry if it came across like that. But trust me, you'll be doing yourself a huge favor by getting a trainer to learn on. Learning to fly on a plane other than a trainer usually means that you'll wind up with a more expensive pile of kindling after the crash.

That's my 2¢ worth

Ken