Self-heating induced failure of graphene devices synthesized from both chemical vapor deposition (CVD) and epitaxial means is compared using a combination of infrared thermography and Raman imaging. Despite a larger thermal resistance, CVD devices dissipate >3x the amount of power before failure than their epitaxial counterparts. The discrepancy arises due to morphological irregularities implicit to the graphene synthesis method that induce localized heating. Morphology, rather than thermal resistance, therefore dictates power handling limits in graphene devices.