I went with enhanced armor for ED-E on my first playthrough, I haven't had a chance to try the weapon upgrade so far, though, so I can't really say which option is preferable.
I went with the damage upgrade for Rex, but since I wasn't playing in hardcoe mode and therefore the only threat was of my companions going unconscious in combat and not being able to help me, I can't say if I'd really recommend that option if you are using hardcoe mode. Because I'd imagine that improving your companion's defensive abilities would be a much more appealing option when there's actually a threat of said companion dying.
Either way, I don't see much point in bothering with the enhanced speed thing since the player still couldn't go any faster, so I'd choose between Lupa's or Rey's brain.