You're partly correct, but partly incorrect -- you can in fact study material to prepare for the LSAT, as it will help you to think in that certain way.
Either way, most people will do worse on the LSAT than on the SAT if you they don't prep, so in that sense, it's clearly more difficult. Among other things, the pool of takers is more competitive.
I did horrible on my SAT's, however i didn't study for them. Percentile wise i think my first non-prep LSAT test, was substantially higher then my actual SAT score.