Strength of Design, at least from an aggregate logit perspective, is quite related to sample size. One way of thinking about it is that losing 18% in "Strength of Design" is similar to losing 18% of your respondents. In other words, interviewing 100 people, but really getting the equivalent of 82 people in worth toward tightening your precision.
But, you have to consider respondent time as well, I believe. It might take respondents more than 18% longer to complete 18 pairs versus 12 triples.
Pairs also induce slightly different choice behavior (and final utilities/attribute importances) than triples. So, choosing between a pairs vs. triples data collection format involves more than just thinking about design efficiency and precision of betas.
I'd strongly encourage you to read a great paper that was given at the Sawtooth Software conference comparing how respondents process information in pairs vs. triples (see Meissner et al., starting on page 151): https://www.sawtoothsoftware.com/download/techpap/2010Proceedings.pdf