I just played through Blood of Gondor for the first time, and a card interaction came up that I'm not sure how to deal with:

The Cross-Roads is a location, put into the staging area by Quest 1A setup. This states "The current quest card gains Siege". There is no requirement to travel to/explore this location before advancing to the next quest stage.

Stage 2B has the "Battle" keyword.

I advanced to stage 2B with the Cross-Roads still in the staging area (I was playing tactics, so having Siege was helping my questing efforts, I had no desire to get rid of it).

At this point, I have a quest stage with Battle AND Siege.

Battle says "Characters use their [Attack] instead of [Willpower] when Questing", and Siege is the equivalent for [Defence].

How does this interaction work?

Hmm, that's an interesting one, I've never had that come up because I cleared out The Cross-Roads before the second stage. You're right that there's no clear answer here. My interpretation of how this is supposed to work is that the siege from the location replaces the battle.

I think they should make a card interaction chart with all card types to show which has priority over which and in which order things must happen.

I believe that you should follow the location keyword. It does not make any difference that the quest card has battle, since there is a location that requires you to make a change in your game , you follow this change. Do not let the battle trait trouble you, it is just another quest card like any other

In my opinion first player decides

I believe that you should follow the location keyword. It does not make any difference that the quest card has battle, since there is a location that requires you to make a change in your game , you follow this change. Do not let the battle trait trouble you, it is just another quest card like any other

That's correct. The card text of Crossroads clearly states that the quest card gets the siege keyword. It doesn't matter that Captured! already has a keyword.