Firstly I think there should be different events, so when you go to a tournament you get to chose Mace, Axe, Sword, Sword & Sheild, Polearm, 2 Handed Sword or Jousting and have an achievement ladder for each event.
I think that this is far more realistic and if the AI is tweaked up properly could add alot more of a challenge, I know I cant be the only 2handed master stuck with a bow while 3 angry swordsman chase me in circles.
Secondly I would like to see a prestige system, keep the town tournmanets the way they are, just free for alls, but add in higher tournaments that you gain access to by touring the smaller towns and gaining a reputation, then on top of that add noble tournaments, only for named knights and thos who carry banners, finally have the annual tournaments that all the lords including the kings converge for, that you only get invited to if your faction ranking is high enough.
I also like the idea of having a huge prize for the annual tournament like a fief or a thoroughbred horse.
Thirdly I think that each combatant should fight with tournament supplied armour and weapon, but at least have a choice as to the basic category of the arm this of course puts more of an emphasis on skill than costly equipment, excepting the joust, I like the idea of the traditional method where if you manage to take a knight of his horse you win it from him, I also think it would add alot of risk if you lost your own mount by being unhorsed
Fourth and finally I think everyone would enjoy a bit of window dressing, this includes Heralds in proper uniform announcing the combatants, a few sound effects for the cheering crowd, a tournament ground with a proper lists not just a small walled paddock, trophies , colourful heraldry for your enemies so you remember who youve beaten and whos beaten you and just little things like pennocells and painted sheilds for decoration.