Question is a bit of a false dichotomy to me. 1v1s are how to figure out the best 1v1 regiments and groupfights will show you which regiment is the better groupfighting regiment. Even then, you're finding out which regiment is doing better on that particular day, as most regiments have their three or four "carries" that can decide rounds that occasionally fail to show up. Other things have changed competitive results, like burnout from doing several events on a single day.
At best, even a mix of groupfighting and 1v1s will show you who the best regiments at single regiment versus single regiment gameplay. That's a small part of the game, glorified as it is. I've seen plenty of 1v1 regiments show up to larger linebattles and get their team killed or just die constantly because they didn't know how to handle working with two other lines and cavalry while dodging cannonballs.
I don't think there is any easy metric to define the best regiments, and there surely is no single event that shows it off. There are too many skills in the game to learn. Duelling, groupfighting, shooting, positioning against one line, positioning against entire enemy teams, fighting infantry, fighting cavalry, dodging artillery without exposing the line, playing sword cav, playing lance cav, groupfighting as cav, shooting cannons, shooting howitzers . . . sure nobody cares about most of these, but surely the "best regiment" is one that can do it all and do it consistently.
Of course, I also think lines should be able to move in double rank without having emotional breakdowns.