I think it was a case that the First Doctor was simply more pragmatic than the Second and Third Doctors. He cut straight through a problem rather than try to figure a way around it like his successors. He also had the luxury of not having to argue with himself.I also found the relations between the Doctors rather odd, though very entertaining. It didn't make much sense that the first Doctor would know what to do when the other two were unsure. After all, they both know more than he does.
Not necessarily, IMO, because of how the Doctor's style changes from one incarnation to the next--especially with the earlier Doctors. The Second Doctor was somewhat messy and prone to improvisation, while the Third Doctor was refined and methodical. It's actually little surprise that they wouldn't like one another. For the Third Doctor, he was likely grateful he wasn't a galactic hobo anymore.I loved the bickering between Two and Three but I also thought that Three's hostility towards Two didn't make much sense. As he was forced by the Timelords to regenerate and didn't want to go, wouldn't he look back more fondly on this incarnation?
Another example was that the Sixth Doctor didn't think too highly of the Fifth Doctor--thought that he was too nice and maybe a bit of a pushover...