First off, is it even valid to conclude that Drive wants to be compared with Taxi Driver? Based on key similarities it almost begs comparison, and to its own misfortune. Early in the film, Gosling's character (who is never named but referred to as "the driver") tells another character that driving is "just part-time." That iconic line automatically makes the viewer remember back to Travis's classic statement. Further, both movies follow the dark journey of a character's decent into violence with a vengeful plot to rescue a girl from a bad situation. In both cases, the mofia is involved. An unlikely character in an unlikely job as a driver of sorts, ends of beating the mob and coming to survive in the end. Even the moment where the audience assumes the Travis is dead is replayed in Drive with a long still shot of the character before he moves.
If there are all these similarities, including iconic lines and scenes, then Drive is begging to be compared, even though it falls flat. While Taxi Driver is introspective and thought-provoking, Drive is surface-level and two dimensional at best. Travis allows for personal introspection through journaling and internal monologues. The driver in Drive is largely silent through most of the film and audience rarely knows what is happening inside his head. When all sounds go completely silent when Travis pulls the trigger as he is pretending in front of the mirror, Taxi Driver forces the audience to actively engage. The long shots of the wet pavement, the overhead tracking shot in the whorehouse, and the frames of blood spatter give the audience ample time to contemplate the movie. The only comparable moments in Drive are the strange dream-like, but real, sequences and a shot with the driver looking through a window on the door from the outside. In the later he is wearing a mask and the audience thinks about how sad his reality is. But, that is it.
One of the most important differences in the two films is the use of violence. Scorsese depicts violence as grotesque and unnatural, just as wrong as Travis's mind. Drive seems to include violence to make it excitingly gory. There is no challenge to the brutality of violence, only the cut-throat reality of mob life. The violence is more of a spectacle than a comment on reality.
Overall, Drive is disappointing compared to Scorsese's incredible piece of art. Drawing explicit parallels to a classic movie sets a high bar that Drive just could not live up to. The movie is worth while for those who are big fans of unnecessary gore or Ryan Gosling's face.