Another big difference between TOR companions and WoW pets is that your companions already come with their own personalities; you don't get to determine more than your relationship with them, be it friendly or...otherwise (one way or the other).
Personally, I find this to be a huge perk. I don't have to work as hard at coming up with a buddy's personality that differs from my own. For example, the womanizing man of leisure companion that consulars get is definitely not a personality I would ever have created on my own. I can't stand him! And yet, he defined himself to me like one of my WoW pets would have: he soloed the boss at the end of the quest chain leading to his becoming a member of my crew while I took out the adds. I genuinely did not think he had it in him. Somehow, because he already had his own personality, this made that accomplishment all the greater. It was perfectly timed, too, since that was the way I accepted him enough to even grudgingly let him aboard my ship. It's amazing; my actual personal feelings toward the character mirror the choices I would have made in game anyway. I can't really describe it better than that.
There's something very real about having a companion whose mind is completely out of your control. They think for themselves, which allows a more genuine response from you and your character. It's an entirely different experience.