High-quality collections of Type II supernova (SN) light curves are scarce because they evolve for hundreds of days, making follow-up observations time consuming and often extending over multiple observing seasons. In light of these difficulties, the diversity of SNe II is not fully understood. Here we present ultraviolet and optical photometry of 12 SNe II monitored by the Las Cumbres Observatory Global Telescope Network during 2013 to 2014, and compare them with previously studied SNe having well-sampled light curves. We explore SN II diversity by searching for correlations between the slope of the linear light-curve decay after maximum light (historically used to divide SNe II into IIL and IIP) and other measured physical properties. While SNe IIL are found to be on average more luminous than SNe IIP, SNe IIL do not appear to synthesize more $\mathrm{<mrow\; data-mjx-texclass="ORD">56</mrow>}$Ni than SNe IIP. Finally, optical nebular spectra obtained for several SNe in our sample are found to be consistent with models of red supergiant progenitors in the 12–16 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ range. Consequently, SNe IIL appear not to account for the deficit of massive red supergiants as SN II progenitors.