Another objective of the interviewer is to confirm your career progression, as well as potentially what you learned from adverse developments.

I too was an experienced hire (14 years of total work experience by the time I interviewed), and chose to follow a modified chronological order, glancing over areas that wouldn't be relevant to a career at BCG.

Nowadays however, I chose to go transversal and simply tell my story by chosing the most relevant examples regardless of which role and company they were from

Which way is right? Both, if done properly. But if in doubt, probably stick to the modified chronological since it is easier to implement and more traditional. Just understand it will make it harder for you to standout however.

I agree with your last statement - this is for them to see how well and concisely you can convey information. It also gives you a chance to highlight what you think is most important. Like you said, I would pick a theme, state that theme, and then highlight the areas in your resume that convey that.

For instance - my "theme" was that I am committed to personal growth in a broad sense (eg many areas of interest). I pointed out how my resume shows this committment and then went a little more specific (like one sentence) to give examples my resume couldn't convey.