In theory, competency based interviews are the best approach - it's fairer if all candidates are asked the same questions, and the interviewer/s are not making any assumptions about the candidate. It's also a reasonable way of getting the feel for whether candidate can expand on what they said in their CV / application or whether it was a load of old flannel.
In theory, it is asking about experience that will be relevant to the job in question rather than a load of hypothetical 'what would you do if...' questions - and a candidate's experience could have been gained from something that's not similar to the current job - some skills / experience suitable for some jobs could have come from voluntary work / studying / caring for relatives and so on.
A downside is that a carefully rehearsed single 'good example' can score higher than a depth of experience across a broad area.
I have had competency based interviews that have felt more like a good natter down the pub (albeit without a pint) with someone in my line of business, talking about stuff I've done in the past and what they / their organisation does (and have had job offers from such interviews.)
I've also had competency based interviews carried out by some HR automaton, who knows very little about the realities of the job, asking very rigid and narrow 'give one example of a time you did X' questions, and basically scoring you on coming out with the buzzwords they have got listed as their 'right' answers. I've tended to be less successful with them...
As with most things in life, there's ways of doing things.