It really depends on what you call "long distance". Anyway, transportation loss for entsoe is public data [1]. You'd need to cross it with production/consumption data [2] in order to get relative numbers.

For instance, France consumed 442 TWh and reported 1.07TWh of losses in 2022, which would be about 2.5% transportation losses.

[1]: https://eepublicdownloads.blob.core.windows.net/public-cdn-c... [2]: https://eepublicdownloads.blob.core.windows.net/public-cdn-c...

Keep also in mind that batteries do two things: They can move loads in time, but they can also reduce transmission capacity requirements by increasing utilisation. As long as there is some time where the transmission line is not fully loaded (which today is true for _any_ transmission line even the limiting ones), then a battery on both ends allows you to use the capacity longer by charging the battery before the bottleneck with excess and once the input falls below discharging the battery to keep the line utilisation high.

The downside of this is that you now have a system that comes with all kinds of nasty additional complexities and failure cases from control theory.