The rules state;
"A player may only play a maximum of one Dragon card during your turn. A player may only play a maximum of one Dragon card during your opponent's game turn. As a result, during the course of any single game turn, there can only be a maximum of two Dragon cards coming into play, one from each player.
In case of contradiction between the effects of two Dragon cards played in succession, the second card trumps the effect of the first one."
So the question is whether there is a contradiction between the effects of the two cards. It could be argued that since the Personal Challenge card player gets a +2 dice modifier, that the defender challenge would go first.
OTOH, if either leader is killed, the 2nd Personal challenge is incapable because it does not meet the minimum requirements. So really for the rules to have meaning, both cards have to be operating together, and the second card trumps the effects of the first card.
So it seems to me that there are a number of possible outcomes, and I'm not sure which would apply;
1. The first played card takes effect, and the 2nd card is taken as not (yet) played.
2. The first played card takes effect, but the modifiers are calculated as per the 2nd played card (modifiers trump)
3. Both cards are taken as played for the same personal challenge combat (both players get the card play modifier)
4. The 2nd played card trumps the first played card entirely, effectively discarding the 1st card. This seems questionable.
I prefer the Option 1. above, but can see the need for a designer response.
“I dreamt of worldly success once.”
― Miyamoto Musashi