I agree with you on the seeming stiffness of the relationship between Obi Wan and Anakin. However, we've also got to take into account the ten years that elapsed between TPM and AOTC. It is possible that they have that friendly sort of relationship and it developed during that time. However, a point was soon reached when they would need to discard the "familiarity" of their acquaintance (as we know friendship to be) and be more master/padawan... a much more professional sort of relationship.

Also, with how little time we actually saw Obi Wan and Anakin together in AOTC, it could also be possible that they do, in fact, still have that more familiar relationship, but the only times they were together in the movie, they were on the hunt (guarding Amidala, hunting down the bounty hunter on Coruscant) and needed to resort to a more dignified relationship for the sake of finishing the task at hand.