Peanut is an important crash crop worldwide, and it is often threatened by drought stress due to unexpected extreme weather events. In this work, NH5 and FH18 were selected as drought-tolerant and drought-sensitive varieties, respectively. Comparison of their physiological responses revealed that NH5 showed less wilting, higher relative water content and lower water loss rate of detached leaves, lower electrolyte leakage, and stronger antioxidant ability under drought stress than did FH18. Based on comparative transcriptomic analysis, 5376 differentially expressed mRNAs were commonly identified in the two varieties, and 2993 genes specifically changed in the drought-tolerant variety and were mainly enriched in photosynthesis-antenna proteins and photosynthetic pathways. Furthermore, 73 microRNAs (miRNAs) were differentially expressed in the drought tolerance variety specifically under drought stress; of these, two key candidate miRNAs, novel miR_416 and novel miR_73, were identified, and the majority of their target genes were enriched in phenylpropanoid biosynthesis, linoleic acid metabolism, and cutin, suberine, and wax biosynthesis. This study lays the foundation for the analysis of the molecular mechanism of drought tolerance and promotes the genetic improvement of peanut drought tolerance.