Solar flares sometimes lead to coronal mass ejections that directly affect Earth's environment. However, a large fraction of flares, including on solar-type stars, are confined flares. What are the differences in physical properties between confined and eruptive flares? For the first time, we quantify the thermodynamic and magnetic properties of hundreds of confined and eruptive flares of GOES class C5.0 and above, 480 flares in total. We first analyze large flares of GOES class M1.0 and above observed by the Solar Dynamics Observatory, 216 flares in total, including 103 eruptive and 113 confined flares, from 2010 until 2016 April; we then look at the entire data set of 480 flares above class C5.0. We compare GOES X-ray thermodynamic flare properties, including peak temperature and emission measure, and active-region (AR) and flare-ribbon magnetic field properties, including reconnected magnetic flux and peak reconnection rate. We find that for fixed peak X-ray flux, confined and eruptive flares have similar reconnection fluxes; however, for fixed peak X-ray flux confined flares have on average larger peak magnetic reconnection rates, are more compact, and occur in larger ARs than eruptive flares. These findings suggest that confined flares are caused by reconnection between more compact, stronger, lower-lying magnetic fields in larger ARs that reorganizes a smaller fraction of these regions’ fields. This reconnection proceeds at faster rates and ends earlier, potentially leading to more efficient flare particle acceleration in confined flares.