I wouldn’t just say international firms. That’s quite broad. Look into the firms practice strengths and THEN the industries/clients they operate within those practice areas.
For instance
Skadden and Bakers both have band 4 ranked debt finance . However
Skadden works on much higher value deals, larger banks and they have a much deeper reputation in the industry than Bakers London who are recently gaining rep after a key lateral hire. To say they are equal competitors I think is a slight push
I don’t believe it’s as simple to name to firms who are both international with shared strengths. Use your LinkedIn contacts to ask people at the firm, go on Legal 500, look at the firm own description of areas to help clarify which firms would really consider each other competitors. I think gaining deeper knowledge will also help u shine at interview. Good luck!