I guess I will offer my 2 cents as a sport pilot of about 15 months with about 225 hours. I trained at a school that specialized in only LSA's and LSA training. My instructor, and she is one of the best, has over 1000 hours in LSA's training. I think this makes all the difference. That school has recently merged with a "traditional" flight school. The upside is that the club now has over 25 aircraft to choose from that range from really nice LSA's to twins and a Cirrus. I will tell you though the mindset amongst the old school at the new school as it were is that LSA's are easy to fly and that they are real pilots so how hard can it be. I really dislike this mindset.
I have had this debate with a friend of mine who is a private pilot. His school says they do sport training. They in fact have a CTLS. They have a range of instructors but none of them even ref that they provide SP training in their bios. They do ref all of the other certificates for which they provide training. This is red flag number one. I am sure they would love to provide training in the CTLS but mostly to get folks to go PPL as they get more hours and also get follow-on instruction business from them. Some of us really only want to get our SP certificates.
I have flown a 172, Cardinal, Zlin (aerobatic bird), Cirrus Sim and also had right seat time in C-130's and RC-135's in the AF all with an instructor or friend in the left seat. All planes follow rules of physics and aerodynamics but all planes do not fly alike. It may just be my perception but the LSA is a challenge to control in landings much more so than those previously mentioned planes. At altitude I find the 172 and larger planes much easier to hold altitude in.
... "when you move to bigger planes you'll be surprised at how ez it is. The bigger planes stay in place"
As a Light Sport Student Pilot with solo privledges I have never really flown a heavier Certified GA Aircraft... thinking to go try a Cirrus (flew a simulator once)... any comments on what to expect flying and landing the real thing compared to something like the PiperSport that I've been flying?