New sunspot data composites, some of which are radically different in the character of their long-term variation, are evaluated over the interval 1845-2014. The method commonly used to calibrate historic sunspot data, relative to modern-day data, is "daisy-chaining", whereby calibration is passed from one data subset to the neighbouring one, usually using regressions of the data subsets for the intervals of their overlap. Recent studies have illustrated serious pitfalls in these regressions and the resulting errors can be compounded by their repeated use as the data sequence is extended back in time. Hence the recent composite data series by Usoskin et al. (2016), $R_{UEA}$, is a very important advance because it avoids regressions, daisy-chaining and other common, but invalid, assumptions: this is achieved by comparing the statistics of "active day" fractions to those for a single reference dataset. We study six sunspot data series including $R_{UEA}$ and the new "backbone" data series $R_{BB}$, recently generated by Svalgaard and Schatten (2016) by employing both regression and daisy-chaining. We show that all six can be used with a continuity model to reproduce the main features of the open solar flux variation for 1845-2014, as reconstructed from geomagnetic activity data. However, some differences can be identified that are consistent with tests using a basket of other proxies for solar magnetic fields. Using data from a variety of sunspot observers, we illustrate problems with the method employed in $R_{BB}$ which cause it to increasingly overestimate sunspot numbers going back in time and we recommend using $R_{UEA}$ because it employs more robust procedures that avoid such problems. ; Comment: In press, Astrophys. J., 2016