Right from the get go the tone is completely different in the two cuts. It's obvious that the original intention was to make the movie as an homage to old 60s/70s crime movies. The music, the font and the cinematography show this really well.
The theatrical cut starts with the operation scene and the monologue, which is pointless and completely ruins the music. It also has some voice added for some reason, and it has a blue filter which ruins the look of the movie.
What the theatrical cut does is that it completely rips the original movie of it's style and homages, and it tries to be a more mainstream action movie. Mel Gibson basically admits this as well. He said that the director's cut was a good movie, but it was the 90s and he wanted a 90s movie. And it shows all the way through the movie.
To make such major changes to a movie after the director/writer already has made the movie is rarely (never?) a good choice. Especially when the director/writer don't even like the changes that are being made.