We analyze full-orbit phase curve observations of the transiting hot Jupiters WASP-19b and HAT-P-7b at 3.6 and 4.5 mu m, obtained using the Spitzer Space Telescope. For WASP-19b, we measure secondary eclipse depths of 0.485% +/- 0.024% and 0.584% +/- 0.029% at 3.6 and 4.5 mu m, which are consistent with a single blackbody with effective temperature 2372 +/- 60 K. The measured 3.6 and 4.5 mu m secondary eclipse depths for HAT-P-7b are 0.156% +/- 0.009% and 0.190% +/- 0.006%, which are well described by a single blackbody with effective temperature 2667 +/- 57 K. Comparing the phase curves to the predictions of one-dimensional and three-dimensional atmospheric models, we find that WASP-19b's dayside emission is consistent with a model atmosphere with no dayside thermal inversion and moderately efficient day-night circulation. We also detect an eastward-shifted hotspot, which suggests the presence of a superrotating equatorial jet. In contrast, HAT-P-7b's dayside emission suggests a dayside thermal inversion and relatively inefficient day-night circulation; no hotspot shift is detected. For both planets, these same models do not agree with the measured nightside emission. The discrepancies in the model-data comparisons for WASP-19b might be explained by high-altitude silicate clouds on the nightside and/or high atmospheric metallicity, while the very low 3.6 mu m nightside planetary brightness for HAT-P-7b may be indicative of an enhanced global C/O ratio. We compute Bond albedos of 0.38 +/- 0.06 and 0 (<0.08 at 1 sigma) for WASP-19b and HAT-P-7b, respectively. In the context of other planets with thermal phase curve measurements, we show that WASP-19b and HAT-P-7b fit the general trend of decreasing day-night heat recirculation with increasing irradiation.