What is the simplest isomorphism invariant which can distinguish between the two non-isomorphic Steiner triple systems on $13$ points?

Train structure and cycle structure, as described [here](http://books.google.co.il/books?id=WVyU94jShHwC&pg=PA231&lpg=PA231&dq=steiner%20system%20isomorphism%20invariant&source=bl&ots=ZkczbSp8ID&sig=t6PLAS6WzJ27kVXD3vNBa8Qyok8&hl=en&sa=X&ei=JY4lU-X-O8jW4ATIhoDABQ&redir_esc=y#v=onepage&q=steiner%20system%20isomorphism%20invariant&f=false), do the job, but is there a simple way? Maybe via $p$-ranks or something like that?