Higher ground will always be an advantage in respect to someone on lower ground for several reasons:
1- FOV (Field of View): Those on high ground have the best FOV , it being limited only by direct interference with it (say a wall , a rock etc) otherwise they can see everything since it's obviously lower, while those on low ground have their FOV limited to same heigth.
2 - Cover: Higher ground will always offer at least partial cover as soon as those on it go prone it will also limit the effectiveness of cover used by those on lower because of that little FOV.
And lots more but that's the basics ...
As for Lightsabers:
1 - Fighting against gravity : if you attack higher ground , you have to fight gravity , a small advantage but every bit counts.
2- Less exposure : When you're on high ground you are only vulnerable Midsection-down to a slash. It's always easier and faster to pivot or jump than to dodge or roll.
My 2 cents on EP III's attack: Anakin is enraged by obi-wan's statement and he TRIES to take the higher ground to prove his "might". Problem is while you jump you can't parry (Usually , unless its a mcgyver movie or such lol).
As for The EP I vs EP III battle , EP 3 >>>> EP I. Think about it, on the whole. EP I: Two jedi have to seek the aid of a semi-retarded, easily scared native to find a boy that defeats a whole Battleship on his own. Nevermind the battle scene (It is pretty cool I agree). Compare it to EP III's plot. GGs lol
Anyway, all the above are oppinions, please challenge them and let's stir some reactions : D .