Dissipative Kerr soliton microcombs are believed to be a promising technique to build a dual-comb source for applications including precision laser metrology, fast laser spectroscopy, and high-speed optical signal processing. In this Letter, we conduct a detailed experimental investigation on the phase coherence between two on-chip Kerr soliton microcombs, where the underlying physical and technical origins that lead to the mutual phase noise between microcombs are analyzed. Moreover, the techniques of 2-point locking and optical frequency division are explored to enhance the dual-microcomb phase coherence, and we demonstrate the best phase noise down to -50 dBc/Hz at 1-Hz offset, -90 dBc/Hz at 1-kHz offset, and -120 dBc/Hz at 1-MHz offset. Our study provides a basic reference for both fundamental studies and practical applications of Kerr soliton dual microcombs that entail high mutual phase coherence.