Time planning is best done in a worst-case scenario, which means that we're looking at (just for matches, not counting striking, character picks, fingerwarming, coaching, etc) a maximum of 18 minutes for a Bo3 with 2/6 in place, versus 24 minutes for a Bo3 with 3/8 in place. Again without looking at in-between activities, a 3/8 set in worst-case takes time that could handle a 33% increase in matches completed under a 2/6 ruleset (three matches in 24 minutes compared to 4 matches in the same). From that stance exclusively, it's fairly clear that 2/6 is more efficient.
But that's not the only stance. Again, players play more defensively when they have more to lose per mistake. I'm not sure about data, but there's a fairly justified opinion floating around that a player will play more aggressively (if it suits their character) when there is more leeway for error. When a mistake will cost you 50% of your total endurance, one will be far less adventuresome when the same mistake could cost at most 33.3repeat% of your total endurance. It remains to be decisively seen (at least in my experience) whether or not the supposed increased aggression from 3stock makes average time less. But it's useful to note that, if such an aggession disparity is proven, then playing with a 6 minute limit means it takes less defensive play to push players toward the time range in which stalling becomes a far more likely solution to the match.
In other words, if we run with the given assumptions, compared to 3/8, 2/6 would result in more defensive play that more quickly reaches the critical point that results in a match going to time due to a time-out strategy. Thus, it would stand to reason, you would have a greater number of games going to time (whether that is desired or not depends almost wholly on a player's experiences, tastes, and the movement speed of their main, but it's fair to say spectators on the whole don't like stalling as a strategy) if you use a 2/6 setup.
Where it matters is whether or not the average match length, weighted by resolution method, is shorter or longer than 3/8. If timeouts only happen in 5% of 3/8 games, and the otherwise average is 3 minutes (depends on matchup, naturally), your average match time is only 3.15 minutes over all. If we say 10% of 2/6 games go to time, and the otherwise average is 3 minutes, you end up with an average of 3.3 minutes per game. Of course, those timeout frequencies and average match lengths are just guesses, but they could analyzed better with actual data, which itself could quite possibly vary region-to-region.
Basically, it's rather impossible to judge meaningfully without real data from both rulesets. Personally, I err on the side of 3/8, but I run a 2-8-person event with only loosely preferential time constraints, not a large tournament. I'd rather some of the larger recurring tournaments toy around with the rules over multiple weeks and keep data on it than for us to jump to 2/6 based on theory alone.