Yeah, the ending is not that good and is also a bit uninspired directed. Also John Dehner, who had some very memorable western roles, is a weak Pat Garrett.
The film was together with Warlock the most bizarre example of psychological characterizations of the 50s, and therefore hated by those who prefered there westerns in a more traditional way. Unfortunately both films are overdoing it by transporting the psychological stuff mainly through pretensious dialogues and Paul Newman is also overdoing the Actors Studio's mannerisms in portraying Billy as a tormented soul. Less had been more for both films, but Arthur Penn was always aiming high in his (anti-) genre films.
Otherwise The Left Handed Gun is a very interesting western, with some exceptional contributions in filming and integrating violence. There is even one slow motion shot, probably the first in an american genre film, which is followed by a remarkable shot from the ground, which shows the boot of the killed deputy, who lies behind, big in the foreground. The impact of the bullet had thrown him out of his boot. I'm somehow sure Leone had seen this image.