You can say that the "left handed" bowline, at the left, is more "simple" than the "right handed", at the right, only in the sense that the path of the line is less convoluted in the former than in the later - it is this 8-shaped part which forms the collar around the rim of the nipping loop that seems to cause the difference you have noticed. However, to see what you mean I had to tie the two knots on the most stiff rope I have, which resist to turn even around three rope diameters ! Otherwise both variations have the same number of tucks, same topology ( "simpler" than the topology of the original, non-TIB version ! ), and are equally easy to remember how to tie as end-of-line locked bowlines. As TIB bowlines, I have no idea which is simpler - I hope that Luca or JP will enlighten us on this...
The thing I like in those TIB bowlines is that the first curves of the standing parts are very wide. ( I do not know other so simple TIB bowlines where the nipping loop encircles three rope diameters (*) - which, supposedly, would be beneficial to the knot s strength.) So, if we chose them for strength, any tendency to remain "open" = not-compact under no or light loading would not be an important issue.
(*) An interesting single TIB bowline - although a little bulky, due to the two collars around the standing end - conceptually simple, and with a wide nipping loop ( that encircles four rope diameters ), is the bowline-with-a-bight ( ABoK#1074) where we make the ( reeved-through-the-nipping-loop ) second bight shrink around the first bight.
