Is the difference between the original meter if 1793 and the latest SI definition important?

I talked about the definition of the meter and the subsequent measures (a gram is a cm³ of water etc) to a group I guided through a French Revolution walking tour, explaining that the metric system was based on easy to observe and replicate phenomenon from which where derived several units.

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I also explained that nowadays, the ease to replicate had been replaced with precision of the object measured. When asked about the difference (would a meter of the revolution be the same as a meter nowadays) I got a bit stumped. I said I didn't knew exactly but I'd guess the new measurement tried to stay as close as possible to the original length, but saying that I felt like it was a bit more arbitrary, like trying to find the work-around to reach the answer we decided beforehand, or, to say it in another way, try to find the exact thing whose measurement would give something as close as possible to the original meter.

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Now I am a historian, specialist of socio-political history, and in no way a physicist. So I wonder if the way to measure things in the International System led to major changes in our understanding of measurements and their applications in daily life (something tangible for everyone, like the height of a building for example)?