How is a correlation coefficient of 0.999992 better than a correlation coefficient of 0.99996 even though both analyses resulted in the same molar absorptivity for the analyte using spectrophotometric analysis? Does 0.999992 result in a higher correlation coefficient than 0.99996? If so, why?

The R² value is a measure of how well your data points fit the trend line. A higher correlation coefficient is better, as it tells you that your result is more precise (even if the numbers you calculate are the same). 

Is the bottom line that both values are nearly perfect straight lines making the differences between the numbers negligible?

Yes.

And with R^2 values that high you are looking at slightly different noise 

What do you mean by slightly different noise?

Perhaps a more meaning insight can be gathered from employing a non-parametric correlation measure.

For example, look at the rank correlations, the so called Spearman Rank correlation statistic. If they are computed here to be 1.000 for both, there is no meaningful difference.

One can also look up the approximate standard deviation measure for R2, and, I would guess, with even a very large sample size , no statistical meaningful difference here as well.