In each version there are five GigaChips unique to that version. The only way to get them for the other version is to trade with a friend, or cheat with a Gameshark or Action Replay card.
Navi Battles and Chips
The one difference here (but it is a large one) is that you fight a different Navi for the Rank 2 item in the DrillMan section of the walkthrough. However, in both versions of the game, the Omega versions of the Navis are still available.
The descriptions of what the different shops sell can be found;