In TPM, Obi-Wan is a 25-year old Padawan who according to Qui-Gon is not yet ready to take the Trials.
Of course, Qui-Gon changes his tune when he finds Anakin and wants to take the Chosen One on as Padawan instead, but since finding and training the Chosen One was quite clearly a huge deal to Qui-Gon, we can assume that his earlier assessment of Obi-Wan was what he really believed about Obi-Wan's readiness.
However, Obi-Wan in TPM certainly seems quite competent. He may not have been really ready to take on a Padawan of his own at that point, but he certainly seemed to have been powerful enough to defeat a Sith, and had plenty of emotional stability and staunch belief in the Force and Jedi Code etc etc.
As such, is there any info in the secondary sources (movie novelizations, Word of Lucas, old scripts etc) about why Qui-Gon considered him still not ready?