Believe it or not, my best friend and I have nearly the exact type of friendship Anakin & Obi do. Both of us have very dominate personalities and both of us are very competitive with each other. It's as much a friendship as it is a rivalry. Anakin & Obi-Wan are best friend due to this. Student is always trying to out match teacher and vise versa. By doing so, it helps bring out the best in both and they rely on each other to keep each other at the top of their game. This is also what is keeping them both alert during war. If they weren't best friends, Anakin wouldn't have been so hurt by seeing Obi emerge from Padme ship in ROTS.I still believe Lucas should have noticed that the script itself was lacking.
A part from that added scene, there was absolutely nothing in that movie that gave us even the slightest hint that Anakin and Obi-Wan were anything other than two guys who couldn't stand each other.
And they were supposed to be best friends.
Besides, Jedi are very stuffy(Besides Quinlan Vos).
I kinda expected friendship between Jedi to be almost Vulcan like.
Also look at Luminaria & Bariss' friendship.
You see bond of respect between them but there is also a cold distance as well.