In Oukoku IV Edit
The cards are large, and they have a weapon and a shield. If you get the sword you go first, and the shield makes you go last.
In 3-2-1 Edit
This time, the cards are more smaller. They are redesigned, and the shield has an up arrow on it.
In Ikari No Tekken Edit
Battle Cards are Flipping Coins. They have a sword and a shield engraved into them. Look closely at the coin to see if you go first or last.
In DX Edit
A shield and a sword are hiding in the chests. You can also use reveal to see the color easily. Red = First, Blue = Last.
In The World Edit
The Battle Cards are back and redesigned. They flip after you press Circle.
In Journey Edit
The Sword and Shield have returned. First now says "Attack", and Last now says "Defend". Reveal now fully shows the cards to you, and you can select a card instead of swapping.
There are no actual strategies (except for using reveals). Thus, they are almost luck-based.